






- 







j- y 












%■ 













*p 















' 













< J 7 V = 







- 



* A 



> :: 



^ V* 





















.- * 









^ * . 













^v*' 



<xV </» 



■ 



■ ^ 












^v c* 









*v 









* V 












oS -70 



> 






u * » I 






v 



EASY LESSONS 
/ 



ON 



REASONING. 



REPRINTED FROM "THE SATURDAY MAGAZINE/' 



NEW EDITION. 



I 



TORONTO : 
COPP, CLARK & CO, 

1872. 






Exchange 
■Western Ont. Univ. Library 

JUL 1 1940 



PREFACE. 



hafnot 8 ^ 8 ^?^- '" the f ° ll0Wing ^ s is one ^ich 

stnZ fo T 7 mtr ° dUCed int ° the C0UrSe of elementary 

studies for young persons of all classes. 

and t a i l S n UPP ° Sed ^ T'' that the difference bet - e - a better 

or on that combined with practice, or on each man's greater 
or less proficiency in the subjects he is treating of. 

cipfe n s d of°Rr,o again COnS - der a SJStematic Stud ? of the Prin- 
ciples of Reasoning as sultable on] t f * 

endowments and of a peculiar turn of mindf and o tho 
only m an advanced stage of their education. 

b/aT Ind tTf f ^"^ " feqUiSite f ° r aH " and is «*-W* 
by all and presents not, necessarily, any greater difficulties 

than .the radim^t. of Arithmetic, G«»«4f^ G»™^" 
all this cannot be so well evinced in an„ .*«. 1 ' 

merit. If the perusal of th Z T * W&7 ** by **"* 



IV PREFACE 

discovery, strictly so called, of anything previously altogether 
unknown, it is possible — since "discovery" is a relative word — 
to be, practically a discoverer, by bringing within the reach of 
thousands some important branch of knowledge of which they 
would otherwise have remained destitute all their lives. 

And in regard to the present subject, a familiar introduction 
to the study is precisely what has been hitherto wanting. 
The existing treatises upon it may be compared to ships well 
freighted, but which can only unlade at a few wharfs, care- 
fully constructed, in advantageous situations. The want is of 
small boats drawing very little water, which can carry ashore 
small parcels of the cargo on every part of the coast, and run 
up into every little creek. 

Should the attempt to supply this deficiency prove as suc- 
cessful, as there is reason, from the trial that has been 
already made (in the Saturday Magazine), to hope, an addi- 
tion by no means unimportant will have been made to the 
ordinary course of elementary education. 

To frame, indeed, a system of rules that should equalize 
persons of all varieties of capacity, would be a project no less 
chimerical in this than in other departments of learning. But 
it would certainly be a great point gained, if all persons were 
taught to exercise the reasoning faculty, as well as the natural 
capacity of each would permit; for there is good reason to 
suspect, that, in this point, men fail quite as often from want 
of attention, and of systematic cultivation of their powers, as 
from natural deficiency. And it is at least worth trying the 
experiment, whether all may not be, in some degree, trained 
in the right exercise of a faculty which all in some degree, 
possess, and which all mast, more or less, exercise, whether 
thoy exercise it well or ill. 

It was at one time contemplated to subjoin an Index of the 
technical terms, with brief definitions of them, and references 
to the Lessons and Sections. But, on second thoughts, it has 
been judged best to omit this, and to recommend each student 



PREFACE. V 

to draw up such an index for himself. It is for students, 
strictly so called, — -that is, persons employed in acquiring an 
elementary knowledge of the subject, — that the work is chiefly 
designed : and for these no exercise could be devised more 
calculated to facilitate their study than that of carefully com- 
piling an Index, and also expanding the Table of Contents, so 
as to give a brief summary of the matter of each Lesson. 
And this being the case, it would not be any real saving of 
labor to the learner, to place before him such an Index and 
Table of Contents already drawn up. 

It may be worth while to suggest to the Teacher to put 
before his pupils, previously to their reading each Lesson, 
some questions pertaining to the matter of it, requiring of 
them answers, oral or written, the best they can think of 
without consulting the book. Next let them read the Lessons, 
having other questions, such as may lead to any needful expla- 
nations, put before them as they proceed. And afterwards let 
them be examined (introducing numerous examples framed by 
themselves and by the teacher), as to the portion they have 
learned, in order to judge how far they remember it. 

Of these three kinds of questions, — which may be called, 
i. Preliminary questions; ii. questions of instruction ; and 
iii. questions of examination, — the last alone are, by a con- 
siderable portion of Instructors, commonly employed. And 
the elementary books commonly known as "catechisms," or 
"books in question and answer," consist in reality of ques- 
tions of this description. 

But the second kind — what is properly to be ealled in- 
structive questioning — is employed by all who deserve to be 
reckoned good teachers. 

The first kind — the preliminary questioning — is employed 
(systematically and constantly) but by few. And at first sight 
it might be supposed by those who have not had experience of 
it, that it would be likely to increase the learner's difficulties. 
But if any well-qualified instructor will but carefully and 



VI PREFACE, 

judiciously try the experiment (in teaching any kind of 
science), he will be surprised to find to how great a degree 
this exercise of the student's mind on the subject will contri- 
bute to his advancement. He will find, that what has been 
taught in the mode above suggested, will have been learnt 
in a shorter time, will have been far the more thoroughly 
understood, and will be fixed incomparably the better in the 
memory. 



CONTENTS. 

[To be filled up by the Student] 
Part T. ANALYTICAL INTRODUCTION. 



Lesson I., p. 13. 



Lesson IL, p. 17. 



Lesson III., p. 22. 



CONTENTS. 

Lesson IV., p. 27. 



Lesson V., p. 31. 



Lesson VI., p. 37. 



Lesson VII., p. 41. 



Lesson VIII., p. 48. 



CONTENTS, IX 



Part II. COMPENDIUM. 



Lesson IX., p. 54 



Lesson X., p. 61, 



Lesson XL, p. 71. 



CONTENTS. 

Lesson XII. , p. 80, 



Lesson XIII., p. 89. 



Lesson XIV., p. 



CONTENTS. Xi 



Part III. SUPPLEMENT. 



Lesson XV., p. 104. 



Part IV. FALLACIES. 



Lesson XVL, p. 117. 



CONTENTS. 



Part Y. DIFFERENT KINDS OF ARGUMENTS. 



Lesson XVII. , p. 134, 



EASY LESSONS ON REASONING. 



PART I. 
ANALYTICAL INTRODUCTION. 



LESSON I. 



N.B. — In these Lessons, whenever two equivalent "words or phrases are 
employed, one of them is enclosed in angular [brackets], instead of the common 
mark of a (parenthesis). 



§ 1. Every one is accustomed more or less to employ 
Reasoning. There is no one that does not occasionally 
attempt, well or ill, to give a Reason for any opinion he 
entertains; — to draw Conclusions from what he sees 
around him, — to support those conclusions by some kind 
of Arguments, good or bad, — and to answer the arguments 
brought against him. 

Now all these expressions, — " giving a reason" — 
"drawing a conclusion" — "bringing forward an argu- 
ment" — relate to one and the same process in the mind, 
that which is properly called " Reasoning." And the 
same may be said of several other expressions also ; such 
as " inferring" or "drawing an inference," — "proving 
a point," — "establishing a conclusion," — "refuting an 
argument," &c. All these expressions, and some others 
besides, have reference, as we have said, to the process of 
Reasoning. 

§ 2. And this process, it is important to observe, is, in 
itself, universally the same; however different the subject- 
matter of our reasoning may be, on different occasions. 

The same is the case with Arithmetic. "We may have 
to add or sub ti act, multiply or divide certain numbers, 
either of Pounds-sterling, or of men, or of bushels of 
corn, &c, but though these are very different things, the 
arithmetical-process itself, in each of the operations, respec- 
tively, is always the same. For instance, to "multiply" 
always means to take one number a certain number of 



14 ANALYTICAL INTRODUCTION. [Part I. 

times ; whether it be men or miles, or days, that we are 
numbering. 

So it is also with Grammar. The Nouns and Verbs 
and other Parts of Speech that Grammar treats of, may 
relate to very different subjects, and may be found in 
various kinds of Compositions ; such as works of Science, 
History, Poetry, &c, but the rules of Grammar are the 
same in all. 

So also the art of Writing (and the same may be said 
of Printing) is in itself the same, however different may 
be the kinds of subject-matter it is employed on. 

Now the same is the case (as has been above said) with 
Reasoning. We may be employed in reasoning on 
human affairs, or on Mathematics, or on Natural-history 
or Chemistry, or other subjects widely different from each 
other. But in every case the Reasoning-process is, in 
itself, the same. 

§ 3. Any Debate [or Disputation,] when you are en- 
deavouring to bring others over to your opinion, is one of 
the occasions on which Reasoning is employed ; and the 
word " arguing" is by some persons understood as having 
reference only to cases where there is a dispute between 
those who are maintaining opposite opinions. But this 
is a mistake. At least, it is a mistake to suppose that 
the use of " Arguments" — if we understand by that, the 
use of Reasoning — is confined to the case of disputes; or 
even that this is the principal employment of it. There 
is no set of men less engaged in dispute and controversy 
than Mathematicians ; who are the most constantly occu- 
pied in Reasoning. They establish all their propositions 
by the most exact proofs ; so complete as not even to 
admit of any dispute. 

And in all other subjects likewise, a sensible man, 
when he wishes to make up his mind on any question 
will always seek for some sufficient " Reason" [or 
" Argument"] on which to found his conclusion. 

Thus, a Judge, before whom any case is tried is occu- 
pied in weighing the Arguments on both sides, that are 
Drought forward by the respective Advocates. He (no 
less than they) is engaged in Reasoning; though the 
Advocates are disputing and the Judge is not. 



Lesson i.] the reasoning-process. 15 

A Physician, again, reasons from what he has read, and 
heard, and seen, in order to draw his conclusions on me- 
dical questions; — a Statesman, in political questions; — a 
Merchant, in mercantile matters ; and so, of the rest. 

§ 4. But when any dispute does take place, between 
persons of opposed opinions, it may be observed that the 
worst educated — those who are the most unskilful in 
reasoning, or in clearly expressing their reasons, — are 
almost always the most apt to grow angry, and to revile 
each other, and quarrel. 

And even when they do not give way to anger, they 
usually, after a long discussion, part, without distinctly 
understanding what the difference between them really 
consists in ; neither of them having clearly expressed his 
own meaning, or fully understood the other's. 

Indeed it often happens that two persons who are dis- 
puting, do, in reality, disagree much less in their opinions, 
than they themselves imagine : or, perhaps not at all. 
And hence it is that the word "misunderstanding" has 
come to signify, a quarrel ; because quarrels so often 
arise from men's not clearly understanding each other's 
meaning. 

Again, it often happens that a person not without good 
sense, will give such weak and absurd reasons for his 
opinion, even when it is a right one, that instead of con- 
vincing others, he will even produce an opposite effect. 

§ 5. In order to avoid such inconveniences, and to con- 
duct the process of Reasoning as clearly, as correctly, 
and as easily, as is possible, it is a great advantage to lay 
down accurate explanations of the principles on which 
Reasoning proceeds, and to employ for the purpose a 
technical language ; that is, a regularly-formed set of 
expressions, distinctly, defined, and agreed on ; and to 
establish certain plain simple rules, founded on, and 
expressed in, this technical language. 

Even in the common mechanical arts, something of a 
technical language is found needful for those who are 
learning or exercising them. It would be a very great 
inconvenience, even to a common carpenter, not to have 
a precise, well-understood name for each of the several 
psrations he p3rf:>rm'4 ; su^li a^ chiseling, sawing, planing, 



16 ANALYTICAL INTRODUCTION. [Part I. 

<fcc, and for the several tools [or instruments] lie works 
with. And if we had not such words as Addition, Sub- 
traction, Multiplication, Division, etc., employed in an 
exactly denned sense, and also fixed rules for conducting 
these and other arithmetical processes, it would be a 
tedious and uncertain work, to go through even such 
simple calculations as a child very soon learns to perform 
with perfect ease. And after all, there would be a fresh 
difficulty in making other persons understand clearly the 
correctness of the calculations made. 

You are to observe, however, that technical language 
and rules, if you would make them really useful, must be 
not only distinctly understood, but also learnt, and re- 
membered as familiarly as the Alphabet; and employed 
constantly, and with scrupulous exactness. Otherwise, 
technical language will prove an encumbrance instead 
of an advantage \ just as a suit of clothes would be, if, 
instead of putting them on and wearing them, you were 
to carry them about in your hand. 

g 6. It has been accordingly found advantageous, in 
what relates to the Reasoning-process, (as well as in. the 
case of mechanical operations, and of calculations,) to 
lay down explanations, and rules, and technical terms ; 
answering to those of Arithmetic, Grammar, and other 
branches of study. 

Amd the technical terms and rules of Grammar, are 
not at all shorter, or easier to be understood and remem- 
bered, than those pertaining to the present subject. 

You may perhaps meet with treatises professing much 
more than what we here propose; — with works pretending 
to teach the right use of "Reason;" (not Reasom'/i^r or 
"Argumentation" merely, but the whole of the Human 
Intellect;) and giving rules for forming a judgment on 
every question than can arise, and for arriving at all truths 
in any subject whatever. But such pretensions, however 
high-sounding and attractive, are fanciful and empty. One 
might as well profess to teach the "right use of the bodily- 
organs," and to lay down a system of rules that should in- 
struct a man in all manual arts and bodily exercises at once. 

If you do but teach a person to ride, or to draw, or to 
spin, <fcc, something is gained ; but if you should profess 



Lesson ii.] the reasoning-process. 17 

to lav down a system of rules to teach all these at once, 
and also the business of a shipwright, and a musician, 
and a watchmaker, and everything else that is done by 
means of the bodily organs, you would teach, in reality, 
nothing at all. 

And so it is on all subjects. It is better to undertake 
even a little, that it is possible to accomplish, than to 
make splendid professions, which can only lead to dis- 
appointment. 

After all. indeed, it cannot be expected, that, in Reason- 
ing, any more than in other mental exercises, men of very 
unequal degrees of intelligence should be brought to the 
same level. Nor is it to be expected, that men will always 
be brought to an agreement in their conclusions. Dif- 
ferent men will have received different information re- 
specting facts ; or will be variously biassed, more or less, 
by their early prejudices, their interests, or their feelings. 

But still, there is something gained, if they are taught 
in respect of the Eleasoning-process itself, how to proceed 
rightly and to express themselves clearly ; and if when 
they do not agree, they can be brought at least to under- 
stand wherein they differ, and to state distinctly, what is 
"the point at issue" (as it is called) between them; that 
is, what is the real question to be decided. 

And it is just so, in the case of Arithmetic also. Two 
persons may differ in their statements of an Account, from 
their setting out with some difference in the numbers each 
puts down; — in the Items (as it is called) of the Account. 
And no rules of Arithmetic can prevent such a difference 
as this. But it is something gained if they are guarded 
(as arithmetical rules do guard us) against differences 
arising out of errors in the calculation itself. 



LESSOR ir. 



§ 1. We have said that in all subjects, and on all occa- 
sions, the Reasoning-process is in itself the same Whether 
you are occupied in refuting an opponent, or in conveying 



18 ANALYTICAL INTRODUCTION. [Part I. 

instruction, or in satisfying your own niind on any point, — 
and again, whatever kind of subject-matter it is that you 
are engaged on, in all cases, as far as you are (in the 
strict sense of the word) reasoning, — that is, employing 
Argument — it is one and the same process (as far as it is 
correctly conducted) that is going on in your own mind. 

And what this process is, must be the next point to be 
inquired into. 

Although (as has been said) all men do occasionally 
reason, they are often, at the time, as unconscious of it as of 
the circulation of their blood, and of the various other pro- 
cesses that may be going on within the body. And even 
when they do, knowingly and designedly, use arguments, 
or are listening to those of another, they will often be as 
much at a loss to explain why one argument appears to 
them strong, and another less strong, and another utterly 
worthless, as if the whole were merely a matter of taste ; 
like their preference of one prospect, or one piece of 
music to another. 

In order, then, to obtain correct rules for forming a 
judgment on this subject, and clear expressions for explain- 
ing such judgment to others, it is necessary to analyse, — 
as it is called, — that is, take to pieces) the Reasoning- 
process. And for that purpose, we should begin by 
examining the most plain, short, and simple arguments, 
and enquiring on what it is that their validity [or con- 
clusiveness] depends ; examining also, some of those 
apparent-arguments which are not valid, and therefore 
not, in reality, arguments at all ; though they are often 
passed off for them, as counterfeit coin is for genuine. 

§ 2. You will perceive, on examination, that what is 
called a " Conclusion," — that is, a proposition proved by 
Argument, — is drawn, in reality, from two other Proposi- 
tions. And these are called its "Premises;" from their 
being (in natural order) "premised" or put before it. 

At first sight, indeed, some might suppose that a 
Conclusion may follow from one Premise alone. For it 
happens, oftener than not, that only one is expressed. 
But in this case, there is always another Premise under- 
stood, and which is suppressed, from its being supposed 
to be fully admitted. 



Lesson ii.J the reasoning-process. 19 

That this is the case, may easily be made evident by 
supposing that suppressed Premise to be denied ; which 
will at one destroy the force of the Argument. For 
instance, if any one, from perceiving that "the World 
exhibits marks of design," infers [or concludes] that " it 
had an intelligent Maker," he will easily perceive, on 
reflection, that he must have had in his mind another 
Premise also, namely, that " whatever exhibits marks of 
design had an intelligent maker:" since if this last pro- 
position were denied, the other would prove nothing. It 
is true, that in some cases one proposition implies another 
by the very signification of the words, to every one 
that understands those words ; as "negroes are men ; 
therefore they are rational-beings," now, "rational-being" 
is implied in the very name "man." And such examples as 
this have led some people into the idea that we reason — 
or that we may reason — from a single Premise. But take 
such a case as this ; some fossil-animal is discovered, which 
Naturalists conclude to have been a "'ruminant," from its 
"ha vino* horns on the skull." Now the laborers wmo duo: 
up the skeleton could not draw this inference, supposing 
they were ignorant of the general law, that "all horned 
animals are ruminant :" — and they might be thus ignorant, 
though using the name "horned animal," in the same 
sense as the Naturalist : for the name itself does not imply 
" ruminant," as a part of its signification ; and again, a 
Naturalist at a distance, who knew the general law, but 
who had heard only an imperfect account of the skeleton, 
and did not know whether it was horned or not, would be 
equally unable to draw the inference. In all cases of what 
is properly called "Argument," there must be two pre- 
mises assumed, whether they are both expressed or not. 

§ 3. Such an argument as the above, when all the 
three propositions are stated at full length, and in their 
natural order, is called a "Syllogism." And this is the 
form in which all correct reasoning, on whatever subject, 
may be exhibited. 

When one of the Premises is suppressed [or under- 
stood^, which, for brevity's sake, is usually the case, the 
argument is called, in technical language, an " Enthy- 
meme;" a name derived from the Greek, and denoting 



20 ANALYTICAL INTRODUCTION. [Part I. 

that there is something left out, which is to be supposed 
[or understood] as being well-known. 

It is to be observed, that, when an argument, stated in 
this last form, is met by opponents, their objection will 
sometimes lie against the assertion itself that is made ; 
sometimes, against its force as an argument. They will 
say either, "I deny what you assume" or "I admit, indeed, 
what you say, but I deny that it proves your conclusion.' ' 
For instance, in the example above, an atheist may be 
conceived either denying* that the World does exhibit 
marks of design, or again, denyingt that it follows from 
thence that it must have had an intelligent Maker. 

Now you are to observe, that these are not in reality 
objections of different kinds. The only difference is, that, 
in the one case, the expressed Premise is denied ; in the 
other, the suppressed Premise. For the force as an argu- 
men, of either Premise, depends on the other Premise. 
If either be denied, the other proves nothing. If both 
be admitted, the Conclusion regularly drawn from them, 
must be admitted. 

§ 4. It makes no difference in respect of the sense of 
an argument, whether the Conclusion be placed last or 
first ; provided you do but clearly mark out what is the 
Conclusion. 

When it is placed last (which is accounted the natural 
order), it is designated by one of those conjunctions 
called "illative" such as "therefore," — "thence," — "con- 
sequently." 

When the Conclusion is put first, the Premise is usually 
called the "Reason;" and this is designated (whether it 
come last or first) by one of the conjunctions called 
"causal" such as "since," — "because," &e. 

And here it is to be observed, that each of these sets 
of conjunctions have also another sense; being used to 
denote, respectively, sometimes " Premise and Conclu- 
sion," — sometimes " Cause and Effect." And much error 
und perplexity have often been occasioned by not attend- 
ing to this distinction. 



* As many of the ancient atheists did. 
f As most of the modern atheists do. 



Lesson ii.] the reasoning-process, 21 

When I say "this ground is rich; because the trees on 
it are nourishing;" or again, when I express the same 
sense in a different form, saving, "the trees on this 
ground are nourishing, and therefore it must be rich," it 
is plain that I am employing these conjunctions to denote 
merely the connexion of Premise and Conclusion ; or (in 
other words) I am implying that the one maybe inferred 
from the other. For it is evident, that the flourishing of 
the trees is not the cause of the ground's fertility, but 
only the cause of my believing it. The richness of the 
soil follows as an inference from the luxuriance of the 
trees ; which luxuriance follows as an effect [or, natural 
consequence] from the richness of the soil. 

But, if again, I say, " the trees flourish because the 
ground is rich," or (which is the same in sense) "the 
ground is rich, and consequently [or therefore] the trees 
flourish,' I am using the very same conjunction in a dif- 
ferent sense; namely, to denote, the Connexion of Cause 
and Effect. For in this case, the luxuriance of the trees 
being a thing evident to the eye, would not need to be 
proved', and every one would understand that I was only 
accounting for it. 

§ 5. But again, there are many cases also in which the 
Cause is employed as an Argument, to prove the existence 
of its effect. So that; the Conclusion which follows, as an 
Inference, from the Premise is also an Effect which follows 
naturally from that same Premise as its Cause. 

This is the kind of argument which is chiefly employed 
when we are reasoning about the future : as for instance 
when, from favorable or unfavorable weather, any one 
infers that the crops are likely to be abundant, or to be 
scanty. 

In such cases, the Cause and the Reason [or Proof] coin- 
cide ; the favorable weather being at once the cause of 
the good harvest, and the cause of our expecting it. 

And this circumstance contributes to men's often con- 
founding together "Cause" and — what is strictly called — 
"Reason;" and to their overlooking the different senses 
If such words as "therefore," "thence," "consequently," 
&c., and again, of such words as "because," "'inasmuch 
as/ &c., and also, of the words "follow," "consequence," 



22 ANALYTICAL INTRODUCTION. [Part I. 

and several others ; which have all of them that double 
meaning which has just been explained. 



LESSON I1L 



§ 1. In such an argument as that in the example 
above given, (in § 2, Lesson ii.) it is clearly impossible 
for any one who admits both Premises to avoid admitting 
the Conclusion. If you admit that " Whatever exhibits 
marks of design had an intelligent Maker," and also 
that "the world exhibits marks of design," you cannot 
escape the Conclusion that "the world had an intelligent 
Maker." 

Or again, if I say "All animals with horns on the head 
are ruminant; the Elk has horns on the head; therefore 
it is ruminant;" it is impossible to conceive any one's 
doubting the truth of the Conclusion, supposing he does 
but allow the truth of each Premise. 

A man may perhaps deny, or doubt, and require proof, 
that all animals thus horned do ruminate. Nay it is 
conceivable that he may even not clearly understand what 
"ruminant" means, or he may have never heard of an 
"Elk;" but still it will not be the less clear to him that 
supposing these Premises granted, the Conclusion must 
be admitted. 

And even if you suppose a case where one or both of 
the Premises shall be manifestly false and absurd, this 
will not alter the conclusiveness of the Reasoning; though 
the conclusion itself may perhaps be absurd also. For 
instance, "All the Ape-tribe are originally descended from 
Reptiles or insects : Mankind are of the Ape-tribe ; there- 
fore Mankind are originally descended from Reptiles or 
Insects ; here, every one* would perceive the falsity of 
all three of these propositions. But it is not the less true 
that the conclusion follows from those premises, and that 
if they were true, it would be true also. 

§ 2. But it oftens happen that there will be a seeming 

* Except certain French Naturalists. 



Lesson iii.] fallacies. 23 

connexion of certain premises with a conclusion which 
does not really follow from them, although, to the inat- 
tentive or unskilful, the argument will appear to be valid. 
And this is most especially likely to occur when such a 
seeming argument [or Fallacy] is dressed up in a great 
quantity of line-sounding words, and is accompanied with 
much vehemence of assertion, and perhaps with expres- 
sions of contempt for anyone who presumes to entertain 
a doubt on the matter. In a long declamatory speech, 
especially, it will often happen that almost any proposi- 
tion at all will be passed off as a proof of any other that 
does but contain some of the same words, by means of 
strenuous assurances that the proof is complete. 

Sometimes again, sound arguments will be distrusted 
as fallacious ; especially if they are not clearly expressed ; 
and the more if the conclusions are such as men are not 
willing to admit. 

And frequently also, when there really is no sound 
argument, the reader or hearer, though he believes or 
suspects that there is some fallacy, does not know how 
to detect and explain it. 

§ 3. Suppose, for instance, such seeming-arguments as 
the following to be proposed: — (1.) " Every criminal is 
deserving of punishment ; this man is not a criminal \ 
therefore he is not deserving of punishment :" or again, 
(2.) "All wise rulers endeavor to civilize the People; 
Alfred endeavored to civilize the People; therefore he 
was a wise ruler." There are perhaps some few persons 
who would not perceive any fallacy in such arguments, 
even when thus briefly and distinctly stated. And there 
are probably many who would fail to perceive such a 
fallacy, if the arguments were enveloped in a cloud of 
words, and conveyed at great length, in a style of vague 
indistinct declamation ; especially if the conclusions were 
such as they were disposed to admit. And others again, 
might perceive, indeed, that there is a fallacy, but might 
be at a loss to explain and expose it. 

Now the above examples exactly correspond respec- 
tively, with the following; in which the absurdity is 
manifest : — (1.) " Every tree is a vegetable ; grass is not 
a tree; therefore it is not a vegetable;" and (2.) "all 



24 ANALYTICAL INTRODUCTION. [Part I. 

vegetables grow ; an animal grows ; therefore it is a 
vegetable." These last examples, I say, correspond 
exactly (considered in respect of the reasoning) with the 
former ones ; the conclusions of which, however true, no 
more follow from the premises than those of the last. 

This way of exposing a fallacy by bringing forward a 
similar one where a manifestly absurd conclusion professes 
to be drawn from premises that are true, is one which 
we may often find it needful to employ when addressing 
persons who have no knowledge of technical rules ; and 
to whom, consequently, we could not speak so as to be 
understood concerning the principles of Reasoning. 

But it is evidently the most convenient, the shortest, 
and the safest course, to ascertain those principles, and 
on them to found rules which may be employed as a test 
in every case that conies before us. 

And for this purpose, it is necessary (as has been above 
said)to analyse the Reasoning process, as exhibited in some 
valid argument expressed in its plainest and simplest form. 

§ 4. Let us then examine and analyse such an example 
as one of those first given: for instance, " Every animal 
that has horns on the head is ruminant; the Elk has 
horns on the head; therefore the Elk is ruminant." It 
will easily be seen that the validity [or "conclusiveness;" 
or "soundness"] of the Argument does not at all depend 
on our conviction of the truth of either of the Premises ; 
or even on our understanding the meaning of them. For 
if we substitute some unmeaning Symbol (such as a letter 
of the alphabet) which may stand for anything that may 
be agreed on — for one of the things we are speaking 
about, the Reasoning remains the same. 

For instance, suppose we say, (instead of "animal that 
has horns on the head,") "Every X is ruminant;" "the 
Elk is X; therefore the Elk is ruminant;" the argument 
is equally valid. 

And again, instead of the word "ruminant," let us put 
the letter "Y:" then the argument "Every X is Y; the 
Elk is X; therefore the Elk is Y;" would be a valid 
argument as before. 

And the same would be the case if you were to put 
"Z" for "the Elk:" for the syllogism "Every X is Y ; Z 



Lesson iii.] arbitrary symbols. 25 

is X; therefore Z is Y," is completely valid, whatever 
you suppose the Symbols, X, Y, and Z to stand for. 

Any one may try the experiment, by substituting for X, 
Y, and Z, respectively, any words he pleases ; and he will 
find that if he does but preserve the same form of expres- 
sion, it will be impossible to admit the truth of the Pre- 
mises, without admitting also the truth of the Conclusion. 
§ 5. And it is worth observing here that nothing is so 
likely to lead to that — very common, though seemingly 
strange — error, of supposing ourselves to understand 
distinctly what in reality we understand but very imper- 
fectly, or not at all, as the want of attention to what has 
been just explained. 

A man reads— or even writes — many pages perhaps, 
of an argumentative work, in which one or more of the 
terms employed convey nothing distinct to his mind : 
and yet he is liable to overlook this circumstance from 
finding that he clearly understands the Arguments. 

He may be said, in one sense, to understand what he 
is reading; because he can perfectly follow the train of 
Reasoning, itself. But this, perhaps, he might equally 
well do, if he were to substitute for one of the words 
employed, X, or Z, or any other such unknown Symbol ; 
as in the examples above. 

But a man will often confound together, the understand- 
ing of the Arguments, in themselves, and. the understanding 
of the ivords employed, and of the nature of the things 
those words denote. 

It appears then that valid Reasoning, when regularly 
expressed, has its validity [or conclusiveness] made evident 
from the mere form of the expression itself, independently 
of any regard to the sense of the words. 

§ 6. In examining this form, in such an example as 
that just given, you will observe, that in the first premise 
("X is Y,") it is assumed universally of the Class of things 
(whatever it may be) which "X" denotes, that " Y" may 
be affirmed of them: and in the other Premise, "Z is 
X") that U Z" (whatever it may stand for) is referred to 
that Class, as comprehended in it. Now it is evident that 
whatever is said for the whole of a class may be said of 
anything that is comprehended [or "included/' or "con- 

B 



26 ANALYTICAL INTRODUCTION. [Part I. 

tained,"] in that Class: so that we are thus authorized 
to say (in the conclusion) that "Z" is "Y." 

Thus also in the example firet given, having assumed 
universally, of the Class of " Things which exhibit marks 
of design/' that they " had an intelligent maker," and 
then, in the other Premise, having referred "The world" 
to that Class, we conclude that it may be asserted of "The 
world" that "it had an intelligent maker." 

And the process is the same when anything is denied 
of a whole Class. We are equally authorized to deny 
the same of whatever is comprehended under that Class. 
For instance, if I say, " No liar is - deserving of trust ; 
this man is a liar ; therefore he is not deserving of trust :" 
I here deny "deserving of trust," of the whole Class 
denoted by the word " liar;" and then I refer "this man" 
to that Class; whence it follows that " deserving of trust" 
may be denied of him. 

§ 7. This argument also will be as manifestly valid, if 
(as in the former case) you substitute for the words which 
have a known meaning, any undetermined symbols, such 
as letters of the alphabet. " No X is Y; Z is X; there- 
fore Z is not Y," is as perfect a syllogism as the other, 
with the affirmative conclusion. 

To such a form all valid arguments whatever may be 
reduced : and accordingly the principle according to which 
they are constructed, is to be regarded as the Universal 
Principle of Reasoning. 

It may be stated, as a general Maxim, thus : " What- 
ever is said, whether affirmatively, or negatively," [or 
" whatever is affirmed or denied"] "of a whole Class may 
be said in like manner," [that is "affirmed in the one 
case, and denied in the other,"] " of everything compre- 
hended under that Class." 

Simple as this principle is, the whole process of Rea- 
soning is embraced in it. Whenever we establish any 
Conclusion, — that is, show that one thing may allowably 
be affirmed, or be denied, of another — this is always in 
reality done by referring that other to some Class of I 
which such affirmation or denial can be made. 

The longest series of arguments, when fully unfolded, 
step by step, will be found to consist of nothing but a I 



Lesson iv.] apparent-arguments. 27 

repetition of the same simple operation here described. 
But this circumstance is apt to be overlooked, on account 
of the brevity with which we usually express ourselves. 
A Syllogism, such as those in the examples above, is 
seldom given at full length ; but is usually abridged into 
an "Enthymeme."* (See Lesson ii. § 3.) And moreover 
what is called "an argument, 11 is very often not one argu- 
ment, but several compressed together; sometimes into a 
single sentence. As when one says: "The adaptation 
of the instinct of suction in young animals to the supply 
of milk in the parent, and to the properties of the Atmo- 
sphere as well as other like marks of design, show that 
the world must have had an intelligent maker." For most 
men are excessively impatient of the tedious formality of 
stating at full length anything that they are already aware 
of, and could easily understand by a slight hint. 



LESSON IV. 



§ 1. We have seen that when an argument is stated in 
the regular form (as in the foregoing examples), which 
is what is properly called a " Syllogism," the validity [or 
conclusiveness] of the reasoning is manifest from the mere 
form of the expression itself, without regard to the sense 
of the words ; so that if letters or other such arbitrary 
anmeaning Symbols, be substituted, the force of the 
argument will be not the less evident. Whenever this is 
not the case, the supposed argument is either sophistical 
and unreal, or else may be reduced (without any alteration 
of its meaning) into the above form : in which form, the 
general Maxim that has been laid down will apply to it. 

What is called an unsound [or fallacious] argument 
(that is an a^are^-argument which is in reality none) 
cannot, of course, be reduced into such a form. But when 
it is stated in the form most nearly approaching to this 
that is possible, and especially when unmeaning symbols 
(such as letters), are substituted for words that have a 
meaning, its fallaciousness becomes evident from its want 
of conformity to the above Maxim. 

* That is, an argument with one of the Premises understood. 



28 ANALYTICAL INTRODUCTION. [Part I. 

§ 2. Let us take the Example formerly given: "Every 
criminal is deserving of punishment ; this man is not a 
criminal; therefore he is not deserving of punishment ;" 
this, if stated in letters, would be, " Every X is Y ; Z is not 
X ; therefore Z is not Y." Here the term (" Y") " deser- 
ving of punishment" is affirmed universally of the Class 
("X") " Criminal;" and it might therefore, according to 
the Maxim, be affirmed of anything comprehended under 
that Class ; but in the instance before us, nothing is men- 
tioned as comprehended under that Class ; only "this man" 
("Z") is excluded from that Class. And although what 
is affirmed of a whole Class may be affirmed of anything 
which that Class does contain, we are not authorized to 
deny it of whatever is not so contained. Eor it is evident 
that what is truly affirmed of a Class, may be applicable 
not only to that Class, but also to other things besides. 

Eor instance, to say that "every tree is a vegetable" 
does not imply that "nothing else is a vegetable." And 
so also, to say that "every criminal is deserving of punish- 
ment" does not imply that "no others are deserving of 
punishment:" for however true this is, it has not been 
asserted in the proposition before us. And in analysing 
an argument we are to dismiss all consideration of what 
might have been asserted with truth, and to look only to 
what actually is laid down in the Premises. 

It is evident, therefore, that such an apparent-argument 
as the above does not comply with the rule [or Maxim] 
laid down ; nor can it be so stated as to comply with it ; 
and it is consequently invalid. 

§ 3. Again, let us take another of the examples formerly 
given; "All wise rulers endeavour to civilize the People; 
Alfred endeavoured to civilize the People ; therefore he 
was a wise ruler." The parallel example to this was, 
"All vegetables grow; an animal grows; therefore it is 
a vegetable." And each of these, if stated in Symbols, 
would stand thus: every "Y is X," [or the thing denoted 
by Y is comprehended under the Class for which X 
stands,] "Z is X; therefore Z is Y." 

Now in such an example, the quality of "growing" 
["X"] is, in one Premise, affirmed universally of "vege- 
table," ["Y"], and it might therefore have been affirmed of 



Lesson iy.] apparent-arguments. 29 

anything that can be referred to the Class of " vegetable" 
as comprehended therein : bnt then, there is nothing re- 
ferred to that Class in the other Premise; only, the same 
thing which had been affirmed of the Class " vegetable," 
is again affirmed of another Class, " animals" (Z); whence 
nothing can be inferred. 

Again, take such an instance as this ; " Fruit is pro- 
duced in England; dates are fruit; therefore dates are 
produced in England." Here "produced in England" is 
affirmed of "fruit," but not universally; for everyone 
would understand you to be speaking not of " all fruit," 
but of "some fruit," as being produced in England. So 
that, expressed in Symbols, the apparent-argument would 
stand thus: "Some X is Y ; Z is X ; therefore Z is Y ;" 
in which you may see that the Rule has not been com- 
plied with ; since that which has been affirmed not of the 
whole of a certain Class, [or, not universally] but only of 
part of it, cannot on that ground be affirmed of whatever 
is contained under that Class. 

§ 4. There is an argument against miracles by the well- 
known Mr. Hume, which has preplexed many persons, 
and which exactly corresponds to the above. It may be 
stated thus: "Testimony is a kind of evidence more 
likely to be false than a miracle to be true;" (or, as it 
may be expressed in other words, we have more reason to 
expect that a witness should lie, than that a miracle should 
occur); " the evidence on which the Christian miracles are 
believed is testimony ; therefore the evidence on which 
the Christian miracles are believed is more likely to be 
false than a miracle to be true." 

Here it is evident, that what is spoken of in the first of 
these Premises is, "some testimony;" not "all testimony," 
[or any ivhatever,] and by "a witness" we understand, 
"some witness," not "every witness;" so that this apparent- 
argument has exactly the same fault as the one above. 
And you are to observe, that it nmkes no difference (as 
to the point now before us) whether the word "some" be 
employed, or a different word, such as "most" or "many," 
if it be in any way said or implied that you are not 
speaking of "all." For instance, "most birds can fly; 
and an ostrich is a bird," proves nothing. 



30 ANALYTICAL INTRODUCTION. [Part I. 

§ 5. In order to understand the more clearly, and to 
describe the more accurately, the fallaciousness of such 
seeming arguments as those of which we have just given 
examples, and also, the conclusiveness of the sound 
arguments, it will be necessary to explain some technical 
words and phrases which are usually employed for that 
purpose. This is no less needful (as was remarked in 
Lesson i.) than for an Artisan to have certain fixed and 
suitable names for the several instruments he works with, 
and the operations he performs. 

The word " Proposition" (which we have already had 
occasion to use) signifies "a Sentence in which something 
is said — [or predicated] — that is affirmed or denied — of 
another." That which is spoken of, is called the "Sub- 
ject" of the Proposition : and that which is said of it, is 
called the "Predicate;" and these two are called the 
" Terms" of the Proposition: from their being (in natural 
order) the extremes [or boundaries] of it. 

You are to observe, that it matters not whether each of 
these Terms consist of one word, or of several. For whether 
a Proposition be short or long, there must always be in 
it, one — and but one — thing of which you are speaking; 
which is called (as has been just said) the Subject of it : 
and there must be (in any one Proposition) one thing, — 
and only one — that is affirmed or denied of that Subject: 
and this which we thus affirm or deny of the other, is 
called — whether it be one word or more — the Predicate. 

§ 6. You are to observe also, that though (in our lan- 
guage) the Subject is usually placed first, this order is not 
at all essential. For instance, "it is wholesome to rise 
early," or "to rise early is wholesome," or " rising early 
is wholesome," are only three ways of expressing the same 
Proposition. In each of these expressions " rising early," 
(or "to rise early," for these are only two forms of the 
Infinitive) is what you are speaking of; and "wholesome'' 
is what you say [or predicate] of it. 

When we state a proposition in arbitrary Symbols, as 
"X is Y," it is understood that the first term ("X") 
stands for the subject, and the last ("Y") for the Pre- 
dicate. But when we use terms that are significant, [or, 
have a meaning] we must judge by the sense of the words 



Lesson v.] propositions. 31 

which it is that is the Subject, and which the Predicate; 
that is we must ask ourselves the question, "What am I 
speaking of; and what am I saying of itT 

For instance; " Great is Diana of the Ephesians;" here 
"great" is evidently the Predicate. Again, "Thou art the 
man;" and "Thou hast given occasion to the enemies of the 
Lord to blaspheme;" by asking yourself the above question, 
you will perceive, that in the former of these examples, 
"Thou" is the Predicate, and in the latter, the Subject.* 

§ 7. That which expresses the affirmation or denial, is 
called the "Copula" For instance, if I say, "X is Y," or 
"X is not Y," in each of these examples, "X," is the 
Subject, and "Y" the Predicate; and the Copula is the 
word "is" in the one, and "is not," in the other. 

And so it is, in sense, though not always in expression, 
in every Proposition. For either the Affirmative-copula, 
"is" or the Negative-copula, "is not," must be always, 
in every Proposition, either expressed in those words, or 
implied in some other expression. 

Any sentence which does not do this — in short, which 
does not affirm or deny — is not a Proposition. For in- 
stance, of these sentences, "Are your brothers gone to 
school 1 ?" "They are not gone;" "Let them go," the second 
alone is a Proposition [or "Assertion"] ; the first being a 
Question, and the last a Command, or Request. 



LESSON V. 



§ 1. We have seen that in every Proposition there is 
something that is spoken of; which is called the subject; 
and something that you affirm or deny of it ; which is 
called the Predicate. And it is evidently of great import- 
ance to understand and express clearly, in each Proposi- 
tion, whether the Predicate is said of the whole of the 
Subject, or only of part of it: — in other words, whether it 
is predicated "universally" or "particularly" [partially.'] 

* The Predicate is the emphatic word or words in each proposition, and 
marked as such, by the voice, in speaking, and sometimes "by Italics or under- 
scoring in writing ; as you may perceive from the examples above, 



32 ANALYTICAL INTRODUCTION. [Part I. 

If, for instance, I say, or am understood to imply, that 
"all testimony is unworthy of credit," this is a very differ- 
ent assertion from saying or implying, merely that "some 
testimony is unworthy of credit." The former of these is 
called a " Universal" Proposition ; the Subject of it being 
taken universally, as standing for anything and everything 
that the term is capable of being applied to in the same 
sense. And a term so taken is said (in technical language) 
to be "distributed.'' 1 The latter of the two is called a 
"Particular Proposition;" the Subject being taken parti- 
cularly, as standing only for part of the things signified 
by it: and the Term is then said to be " undistributed '." 

The technical word " distributed" (meaning what some 
writers express by the phrase "taken universally" is used, 
as you perceive, in a sense far removed from what it bears 
in ordinary language. But, — for that very reason, — it is 
the less likely to lead to mistakes and confusion. And 
when once its technical sense is explained, it is easily re- 
membered. When I say "birds come from eggs," and 
again, "birds sing," I mean, in the former proposition, 
"all birds" [or "every bird"]; in the latter proposition 
I mean, not "all" but "some" birds. In the former case 
the term "birds" is said to be "distributed;" in the latter, 
"undistributed." You must be careful also to keep in 
mind the technical sense (already explained) of the word 
"particular." In ordinary discourse, we often speak of 
"this pa/rticular person" or thing; meaning "this indivi- 
dual." But the technical sense is different. If I say, 
"this city is large" the Proposition is not "Particular," 
but is equivalent to a Universal ; since I am speaking of 
the whole of the Subject ; which is "this single city" But 
"some city is large," or "some cities are large" is a parti- 
cular proposition; because the Subject, "city" is taken 
not universally, but partially. 

The distinction between a "Universal" proposition and 
a "Particular," is (as I have said) very important in Rea- 
soning; because, as has been already remarked, although 
what is said of the whole of a Class may be said of any- 
thing contained in that Class, the Rule does not apply 
when something is said merely of a part of a Class. (See 
the example "X is Y" in § 3 of the preceding Lesson.) 



Lesson v.] quantity and quality. 33 

§ 2. You will have seen that in some of the foregoing 
examples, the words "all," " every," or "any," which are 
used to denote the distribution of a Subject, and again, 
"some," which denotes its non-distribution, are not ex- 
pressed. They are often understood, and left to be sup- 
plied in the reader's or hearer's mind. Thus, in the last 
example, "birds sing," evidently means "some birds;" 
and "man is mortal" would be understood to mean 
"every man." 

A Proposition thus expressed, is called "Indefinite ;" 
it being left undetermined ["undefined"] by the form of 
expression, whether it is to be considered as Universal or 
as Particular. And mistakes as to this point will often 
given a plausible air to fallacies ; such as that in the last 
lesson (§4) respecting "Testimony." 

Bat it is plain, that every proposition must in reality 
be either Universal or Particular [that is, must have its 
Subject intended to be understood a 3 distributed, or, as 
not distributed]; though we may not be told which of 
the two is meant. 

And this is called, in technical language, the distinction 
of Propositions according to their "Quantity;" namely, 
into Universal and Particular. "Every X is Y" and 
" some X is Y," are propositions differing from each 
other in their "quantity," and in nothing else. 

§ 3. But the Predicate of a proposition, you may ob- 
serve, has no such sign as "all" or "some," affixed to it, 
which denote, when affixed to the Subject, the distribution 
or non-distribution of that term. And yet it is plain that 
each Term of a proposition — -whether Subject or Predicate 
— must always be meant to stand either for the whole, or 
for part, of what is signified by it; — in other words, — 
must really be either distributed or undistributed. But 
this depends, in the case of the Predicate, not on the 
"quantity" of the proposition, but on what is called its 
" Quality ;" that is, its being Affirmative or Negative. And 
the invariable rule (which will be explained presently) is, 
that the Predicate of a Negative-proposition is distributed 
and the Predicate of an Affirmative, undistributed. 

When I say "X is Y," the term "Y" is considered as 
standing for part of the things to which it is applicable ; 



34 ANALYTICAL INTRODUCTION. [Part I. 

in other words, is "undistributed." And it makes no dif- 
ference as to this point whether I say "all X," or "some 
X is Y." The Predicate is equally undistributed in both 
cases; the only thing denoted by the signs "all" or "some/' 
being the distribution or non-distribution of the Subject. 

If, on the other hand, I say, "X is not Y," whether 
meaning, that "No X is Y," or that "some X is not T," 
in either case "Y," is distributed. 

§ 4. The reason of this rule you will understand, by 
considering, that a term which may with truth be affirmed 
of some other, may be such as would also apply equally 
well, and in the same sense, to something else besides that 
other. Thus, it is true that "all iron is a metal," 
although the term "metal" is equally applicable to gold, 
copper, &c, so that you could not say with truth that 
"all metal is iron," or that "iron, and that only, is a 
metal." For the term "iron" is of narrower extent than 
the term "metal;" which is affirmed of it. 

So that, in the above proposition, what we have been 
comparing, are the whole of the term "iron," and part of 
the term "metal;" which latter term, consequently, is 
undistributed. 

And this explanation applies to every affirmative pro- 
position. For though it may so happen that the Subject 
and the Predicate may be of equal extent [or "equivalent;" 
or as some express it, "convertible"] so that the Predicate 
which is affirmed of that Subject could not have' been 
affirmed of anything else, this is not implied' in the expres- 
sion of the proposition itself. 

In the assertions, for instance, that " every equilateral 
triangle is equiangular," and that "any two triangles which 
have all the sides of one equal to all the sides of the other, 
each to each, are of equal areas," it is not implied that j 
"every equiangular triangle is equilateral," or that "any 
two triangles of equal areas, have their respective sides 
equal." This latter, indeed, is not true: the one preceding 
it is true : that is, it is true that "every equiangular triangle 
is equilateral," as well as that "every equilateral triangle 
is equiangular:" but these are two distinct propositions, 
and are separately proved in treatises on Geometry." 
If it happen to be my object to assert that the Predicate 



Lesson v.] convertible terms. 35 

as well as the Subject of a certain affirmative proposition 
is to be understood as distributed — and if I say, for 
instance, "all equilateral triangles, and no others, are 
equiangular," — I am asserting, in reality, not one pro- 
position merely, but tivo. And this is the case whenever 
the proposition I state is understood (whether from the 
meaning of the words employed, or from the general drift 
of the discourse) to imply that the whole of the Predicate 
is meant to be affirmed of the subject. 

Thus, if I say of one number — suppose 100 — that it is 
the Square of another, as 10, then this is understood by 
every one, from his knowledge of the nature of numbers, to 
imply, what are, in reality, the two propositions, that "100 
is the Square of 10," and also that "the Square of 10 is 100." 

Terms thus related to each other are called in technical 
language u convertible" [or "equivalent"] terms.* But 
then, you are to observe that when you not only affirm 
one term of another, but also affirm (or imply) that these 
are " convertible" terms, you are making not merely one 
assertion, but tivo. 

§ 5. It appears, then, that in affirming that " X is Y," 
I assert merely that " Y," either the whole of it, or party 
(it is not declared which), is applicable to "X;" [or 
"comprehends," or "contains" X]. Consequently, M any 
part of a certain Predicate be applicable to the Subject, it 
must be affirmed, — and of course cannot be denied — of 
that Subject. To deny, therefore, the Predicate of the 
Subject, must imply that no part of the Predicate is 
applicable to that Subject; in short, that the whole 
Predicate is denied of that Subject. 

You may thus perceive that to assert that "X is not 
Y," is to say that no part of the term " Y" is applicable 
to "X;" (for if any part were applicable, "Y" could be 
affirmed, and not denied of "X :") in other words, that the 
whole of "Y" is denied of "X;" and that consequently 
"Y" is "distributed." When I say for instance, "All the 
men found on that island are sailors of the ship that was 



* In any language which has a definite article — as "the" in English, — this 
denotes that the terms are convertible. In Latin, which has no article, we ax© 
left to judge from the context. 



36 ANALYTICAL INTRODUCTION. [Part I. 

wrecked there," tliis might be equally true whether the 
whole crew or only some of them were saved on the 
island. To say, therefore, that "the men found on that 
island are not sailors of the ship," &c, would be to deny 
that any part of that crew are there ; in short, it would 
be to say that the whole of that Predicate is ^applicable 
to that subject. 

§ 6. And this holds good equally whether the negative 
proposition be "universal" or "particular." For to say 
that some "X is not Y" (or — which is the same in sense 
— that "All X is not Y") is to imply that there is no 
part of the term "Y" [no part of the class which "Y" 
stands for\ that is applicable to the whole without excep- 
tion, of the term "X;" — in short, that there is some part 
of the term "X" to which " Y" is wholly inapplicable. 

Thus, if I say "some of the men found on that island 
are not sailors of the ship that was wrecked there/' or, in 
other words, "the men found on that island are not, all 
of them, sailors of the ship," &c, I imply that the term 
" sailors," &c, is wholly inapplicable to some of the "men 
on the island;" though it might, perhaps, be applicable 
to others of them. 

Again if I say "some coin is made of silver," and 
"some coin is not made of silver" (or, in other words, that 
"all coin is not made of silver") in the former of these 
propositions I imply, that in some portion (at least) of the 
Class of " things made of silver," is found [or compre- 
hended] "some coin:" in the latter proposition I imply 
that there is "some coin" which is contained in no portion 
of the Class of "things made of silver;" or (in other words) 
which is excluded from the whole of that Class. So that 
the term "made of silver" is distributed in this latter 
proposition, and not, in the former. 

Hence may be understood the Rule above given, that in 
all Affirmative-propositions the Predicate is undistributed 
and in all Negative-propositions, is distributed. 

The "Subject" is, as we have seen above, distributed 
in a Universal -proposition (whether affirmative or nega- 
tive) and not in a Particular. So that the distribution 
or non-distribution of the Subject depends on the " Quan- 
tity 1 of the proposition, and that of the Predicate, on the 
"Quality." 



Lesson vi.] terms of a syllooism. 37 



LESSON VI. 



§ 1. The next thing to be learnt and remembered is 
the names of the three Terms that occur in a Syllogism. 
For you will have perceived from the foregoing examples, 
that there are always three terms ; which we have desig- 
nated by the Symbols X, Y, and Z. Each Syllogism 
indeed has, in all, three Propositions ; and every Pro- 
position has two Terms ; but in a Syllogism each Term 
occurs twice; as, " X is Y ; Z is X ; therefore Z is Y." 

Of these three Terms then, that which is taken as the 
Subject of the Conclusion ("Z") is called the "Minor- 
term;" the Predicate of the conclusion (" Y") is called the 
"Major-term;" (from its being usually of more extensive 
signification than the " Minor," of which it is predicated;) 
and the Term ["X"] which is used for establishing 
the connexion between those two, is thence called the 
"Middle-term " [or "medium of proof "~\ 

Of these two Premises, that which contains the Major- 
term, ("X is Y,") is called the " Major premise ;" (and it 
is, properly, and usually, placed first; though this order 
is not essential;) and that which contains the Minor-term 
("Z is X") is called the "Minor-premise" And in these 
two premises, respectively, the Major-term and Minor- 
term are, each, compared with the Middle-term, in order 
that, in the Conclusion, they may be compared with each 
other ; that is, one of them affirmed or denied of the 
other. 

§ 2. Xow it is requisite, as you will see, by looking 
back to the examples formerly given, that, in one or other 
of the Premises, the Middle-term should be distributed. 
For if each of the terms of the Conclusion had been com- 
pared only with part of the Middle-term, they would not 
have been both compared with the same ; and nothing 
could thence be inferred. 

Thus, in one of the above examples, when we say "food" 
(namely, "some food,") "is necessary to life," the term 
"food" is undistributed, as being the Subject of a Parti- 
cular-proposition; in other words, we have affirmed the 



38 ANALYTICAL INTRODUCTION. [Part I. 

term " necessary to life," of part only, not the whole, of 
the Class denoted by the term "food;" and again, when 
we say "corn is food" the term "food" is again undistri- 
buted, (according to the Rule given in the last Lesson), 
as being the Predicate of an Affirmative ; in other 
words, though we have asserted that the term "food" is 
applicable to "corn," we have not said (nor, as it happens, 
is it true) that it is not applicable to anything else ; so 
that we have not been taking this term "food" universally, 
in either Premise, but, each time, " particularly." And 
accordingly nothing follows from those premises. 

So also, when it is said, "A wise ruler endeavours to 
civilise the People ; and Alfred endeavoured to civilise the 
People :" [or, " Y is X, and Z is X;"] the Middle-term 
is here twice made the Predicate of an Affirmative pro- 
position, and consequently is left undistributed, as in the 
former instance ; and, as before, nothing follows. For, 
(as was formerly observed) we are not authorized to affirm 
one term of another, merely on the ground that there is 
something which has been affirmed of each of them ; as 
the term " growing" (in the example formerly given) is 
affirmed of "vegetables" and also of "animals.''' 

In each of these cases then, such an apparent argument 
is condemned on the ground that it "has the middle-term 
undistributed" 

§ 3. The other kind of apparent Syllogism formerly 
given as an example, is faulty (as was then shown) from 
a different cause, and is condemned under a different 
title. " Every tree is a vegetable ; grass is not a tree, 
therefore it is not a vegetable ;" or, "Every X is Y ; Z 
is not X ; therefore Z is not Y." 

Here, the middle-term "X" is distributed; and that, 
not only in one premise, but in both ; being made, first, 
the subject of a Universal proposition, and again, the 
Predicate of a negative. But then, the Major-term, 
"Y" which has not been distributed I in the Premise, is yet 
distributed in the Conclusion ; being in the Premise, the 
Predicate of an Affirmative, and, in the Conclusion, of a 
Negative. We have therefore merely compared part of 
the term ["Y"] "vegetable" with the Middle-term "Tree;" 
["X;"] and this does not authorize our comparing, in the 



Lesson vi.] terms of a syllogism. 



39 



Conclusion, the whole of the same term with [Z] "grass;" 
which, as was explained above, we must do, if we deny 
the term " grass" of "vegetable." 

Nothing therefore follows from the Premises ; for it is 
plain that they would not warrant an affirmative Conclu- 
sion. To affirm that " grass is a vegetable," (or, as one 
might equally well, that "a house is a vegetable,") because 
it "is not a tree," would not have even any appearance 
of Seasoning. ~No one would pretend to affirm one term 
of another (as Y, of Z) on the ground that it had been 
affirmed of something ("X") which had been denied of 
that other. 

Such a fallacy as the one we have been above consider- 
ing, is condemned as having what is called in technical 
language, an " illicit process;" that is an unauthorised 
proceeding, from a term, ^.^distributed in the Premise, to 
the same term, distributed, in the Conclusion : or, in other 
words, taking a term more extensively in the Conclusion 
than it had been taken in the Premise; which is, in fact, 
introducing an additional term. 

§ 4. The examples that have been all along given, both 
of correct-reasoning and of Fallacy, have been, designedly, 
the simplest and easiest that could be framed. And hence, 
a thoughtless reader, observing that the rules given, and 
the technical language employed, though not difficult to 
learn, are yet less easy than the examples themselves to 
which these are applied, may be apt to fancy that his 
labor has been wasted; and to say, "Why common sense 
would show any one the soundness of the reasoning, or the 
unsoundness, in such examples as these, with less trouble 
than it costs to learn fche rules, and the technical terms." 
And a beginner of Arithmetic might say the same. For 
the examples usually set before a learner, are, purposely, 
such easy questions as he could answer " in his head" (as 
we say) with less trouble than the arithmetical rules cost 
him. But then, by learning those rules, through the 
means of such simple examples, he is enabled afterwards 
to answer, with little difficulty, such arithmetical ques- 
tions as would be perplexing and laborious, even to a 
person of superior natural powers, but untaught. 

It is the same, in the learning of a foreign Language. 



40 ANALYTICAL INTRODUCTION. [Part I. 

The beginner has to bestow more pains on the transla- 
ting of a few simple sentences, than the matter of those 
sentences is worth. But in the end, he comes to be able 
to read valuable books in the Language, and to converse 
with intelligent foreigners, which he could not otherwise 
have done. 

And so also, in the present case, it will be found, that, 
simple as are the examples given, not only all valid 
Reasoning, on whatever subjects, may be exhibited, and 
its validity shown, in the form that was first put before 
you, but also, most of the Sophistical arguments [Fal- 
lacies] by which men are every day misled, on the most 
important subjects, may be reduced into the same forms 
as those of the examples lately given. 

Hume's argument against Miracles as believed on 
Testimony, which was explained in a former lesson, is an 
instance of this. And numberless others might be given. 

§ 5. For example, there is an erroneous notion com- 
monly to be met with, which is founded on a fallacy that 
may be thus exhibited as a case of undistributed middle 
term: "A man who is indifferent about all religion, is 
one who does not seek to force his religion on others ;" (for 
though this is far from universally true, it is commonly 
believed;) " this man does not seek to force his religion on 
others; therefore he is indifferent to all religion." 

Again, as an example of the other kind of fallacy above- 
mentioned, the " illicit process" of the Major-term, we may 
exhibit in that form the sort of reasoning by which one 
may suppose the Priest and the Levite, in the Parable 
of the Good Samaritan, to have satisfied themselves that 
the poor wounded stranger had no claim on them as a 
neighbor; — a kind of procedure of which one may find 
instances in real life in all times : 

" A kinsman or intimate acquaintance has a claim to 
our neighborly good-offices : this man, however, is not a 
kinsman, (fee, therefore he has no claim," <fcc. Again, " A 
Nation which freely admits our goods ought to be allowed 
freely to supply us with theirs : but the French do not 
freely admit our goods : therefore," &c. Again, "Nations 
that have the use of money, and have property in land, 
are subject to the evils of avarice, of dishonesty, and of 



Lesson vii.] common-terms. 41 

abject poverty; but savage nations have not the use of 
money," &c, &c. 

And again, " A kind and bountiful landlord ought to 
be exempted from lawless outrage; but this man is not a 
kind and bountiful landlord; therefore," &c. 

It will be found a very useful exercise to select for your- 
self a number of other arguments, good or bad, such as are 
commonly to be met with in books or conversation ; and 
to reduce them to the most regular form they will admit 
of, in order to try their validity by the foregoing rules. 

You must keep in mind, however, (what was said in the 
first Lesson) that technical terms and rules will be rather 
an incumbrance than a help, unless you take care not 
only to understand them thoroughly, but also to learn 
them so perfectly that they may be as readily and as 
correctly employed as the names of the most familiar 
objects around you. 

But if you take the trouble to do this once for all, you 
will find that, in the end, much trouble will have been 
saved. For, the explanations given of such technical- 
terms and general rules, when thoroughly learnt once, will 
save you the necessity of going through nearly the same 
explanation, over and over again, on each separate occasion. 

In short, the advantage of technical-terms is just like 
what we derive from the use of any other Common-terms.^ 

When, for instance, we have once accurately learnt the 
definition of a " Circle," or have had fully described to us 
what sort of creature an "Elephant" is, to say, "I drew 
a Circle," or " I saw an Elephant," would be sufficiently 
intelligible, without any need of giving the description or 
definition at full length, over paid over again, on every 
separate occasion. 



LESSON VII. 



§ 1. We have seen that all sound Reasoning consists in 
referring that of which we would (in the conclusion) affirm 
or deny something, to a Class, of which that affirmation or 

* This will be more fully explained in the subsequent Lessons. 



42 ANALYTICAL INTRODUCTION. [Part I. 

denial may be made. 'Now, the " referring of anything 
to a class," means (as you will perceive on looking back 
to the examples that have been given) to affirm of it a 
term denoting a Class; which Term, you will have observed, 
is the Middle-term of the Syllogism. 

We are next led therefore to inquire what terms may 
be affirmatively predicated of what others. 

It is plain that a proper-name, or any other term that 
stands for a single individual, cannot be affirmed of 
anything except that very individual. For instance, 
"Romulus"— the "Thames"— "England"— "the founder 
of Rome" — "this river," <fec, denoting each, a single 
object, are thence called "Singular terms:" and each of 
them can be affirmed of that single object only, and may, 
of course, be denied of anything else. 

When we say "Romulus was the founder of Rome," we 
mean that the two terms stand for the same individual. 
And such is our meaning also when we affirm, that "this 
river is the Thames." 

On the other hand, those terms which are called "Com- 
mon" (as opposed to "Singular") from their being capable 
of standing for any, or for every, individual of a Class, — 
such as "man," "river," country" — may of course be 
affirmed of whatever belongs to that Class : as, "the Thames 
is a river;" "the Rhine and the Ganges are rivers." 

And observe that throughout these Lessons we mean 
a "Class" not merely a Head or general description to 
which several things are actually referred, but one to 
which an indefinite number of things might, conceivably, 
be referred : namely, as many as, (in the colloquial phrase) 
may "'answer to the description." For instance, we may 
conceive that when the first created man existed alone, 
some beings of a Superior Order may have contemplated 
him, not merely as a single individual bearing the proper- 
name "Adam," but also (by Abstraction, which we shall 
treat of presently) as possessing those attributes which 
we call collectively, "human nature;" and they may have 
applied to him a name — such as "Man" — implying those 
attributes [that "description"^, and nothing else; and 
which would consequently suit equally well any of his 
descendants. 



Lesson vii.] common-terms. 43 

When therefore anything is said to be "referred to 
such and such a Class/' we mean either what is, or what 
might be a Class, comprehending any objects that are " of 
a certain description;" which description (and nothing 
else) is implied by the " Common-term" which is a name 
of any, or all, of those objects. 

§ 2. A Common-term is thence called (in relation to 
the "Subjects" to which it is applicable) a "Predicate;" 
that is affirmatively-^redicahle ; from its capability of 
being affirmed of another Term. 

A Singular term, on the contrary, may be the Subject 
of a proposition, but not the Predicate : unless of a 
Negative-proposition ; (as "the first-born of Isaac was not 
Jacob;") or unless the Subject and Predicate be merely 
two expressions for the same individual ; as in some of 
the examples above. 

You are to remember, however, that a Common-term 
must be one that can be affirmed of an indefinite number 
of other terms, in the same sense, as applied to each of 
them : as "vegetable" to "grass," and to an " oak." For 
different as these are, they are both " vegetables" in the 
same sense : that is, the word "vegetable" denotes the 
same thing in respect of both of them: [or, "denotes 
something common to the two."] 

But there are several proper-names which are borne, 
each, by many individuals; such as "John," "William," 
&c, and which are said to be (in ordinary discourse) very 
common names ; that is, very -frequent. But none of these 
is what we mean by a " Common term ;" because, though 
applied to several persons, it is not in the same sense, but 
always as denoting, in each case, one distinct individual. 

If I say, "King Henry was the conqueror at Agincourt," 
and, "the conqueror of Bichard the Third was King 
Henry," it is not, in sense, one term, that occurs in both 
those propositions. But if I say, of each of these two 
individuals, that he was a "King," the term "King" is 
applied to each of them in the same sense. 

§ 3. A Common-term, such as "King," is said to have 
several " Significates ;" that is, things to which it may be 
applied : but if it be applied to every one of these in the 
same sense, [or denotes in each of them the same thing] 



44 ANALYTICAL INTRODUCTION. [Part I. 

it lias but one "signification" And a Common-term thus 
applied, is said to be employed "uni vocally." 

If a term be used in several senses, it is, in meaning, 
not one term only, but several. Thus, when " Henry" (or 
any other such name) is applied to two individuals to 
denote, in each case, that one distinct person, it is used 
not as one term, but as two; and it is said to be applied 
to those two, "equivocally" 

The like often occurs in respect of Common-terms also; 
that is, it offcens happens that one word or phrase, will 
be not merely one, but several Common-terms. 

Take for example the word " Case," used to signify a 
kind of "covering " and again (in Grammar) an inflection 
of a noun: (as "him" is the accusative [or objective] case 
of "he;") and again a "case" such as is laid before a 
lawyer. The word is, in sense, three; and in each of 
the three senses may be applied " univocally" to several 
things which are, in that sense, signified by it. But when 
applied to a box and to a grammatical case, it is used 
1 'equivocally." 

§ 4. That process in the mind by which we are enabled 
to employ Common- terms, is what is called " Generaliza- 
tion;" Common-terms being often called also " General- 
terms" 

"When in contemplating several objects that agree in 
some point, we "abstract" [or draw off] and consider 
separately that point of agreement, disregarding every- 
thing wherein they differ, we can then designate them 
by a Common-term, applicable to them, only in respect of 
that which is "common" to them all, and which expresses 
nothing of the differences between them. And we obtain 
in this way, either a term denoting the individuals them- 
selves thus agreeing considered in respect o/that agreement, 
(which is called a co ncr ete-common-teYm), or again, a 
term denoting that circumstance itself wherein they agree ; 
which is called an abstract-common-teYm. 

Thus we may contemplate in the mind several different 
" kings" putting out of our thoughts the name and indivi- 
dual character of each, and the times and places of their 
reigns, and considering only the regal Office which belongs 
to all and each of them. And we are thus enabled to 



Lesson vii.] common-terms. 45 

designate any or every one of them by the " common" [or 
general] term, "king:" or again by the term " royalty" 
we can express the circumstance itself which is common 
to them. And so in the case of any other common-term. 

The "Abstraction" which here takes place, is so called 
from a Latin- word originally signifying to "draw off;" 
because we separate, and as it were, draw off, in each of 
the objects before us, that point — apart from every other 
— in which they are alike. 

It is by doing this, that " Generalization" is effected. 
But the two words have not the same meaning. For 
though we cannot "generalize" without "'abstracting" we 
may perform Abstraction without Generalization. 

§ 5. If, for instance, any one is thinking of " the Sun," 
without having any notion that there is more than one 
such body in the Universe, he may consider it without 
any reference to its place in the sky ; whether rising or 
setting or in any other situation; (though it must be 
always actually in some situation;) or again, he may be 
considering its heat alone, without thinking of its light ; 
or of its light alone ; or of its apparent magnitude ; 
without any reference either to its light or heat. ]S"ow 
in each of these cases there would be Abstraction ; though 
there would be no Generalization, as long as he was 
contemplating only a single individual; that which we 
call the "Sun." 

But if he came to the belief (which is that of most 
Astronomers) that each of the fixed Stars is a body afford- 
ing light and heat of itself, as our Sun does, he might 
then, by absracting this common circumstance, apply to all 
and each of these (the Sun of our System and the Stars) 
one common-term denoting that circumstance ; calling 
them all " Suns." And this would be, to "generalize." 

In the same manner, a man might, in contemplating a 
single mountain, (suppose, Snowdon), make its height 
alone, independently of everything else, the subject of his 
thoughts ; or its toted bulk ; disregarding its shape and 
the substances it is composed of ; or again, its shape alone; 
and yet while thus abstracting he might be contemplating 
but the single individual. But if he abstracted the cir- 
cumstance common to Snowdon, Etna, Lebanon, (fee, and 



46 ANALYTICAL INTRODUCTION. [Part I. 

denoted it by the common-term "Mountain," lie would 
then be said to generalize. He would then be considering 
each, not as to its actual existence as a single individual, 
but as to its general character, as being of such a descrip- 
tion as would apply equally to some other single objects. 

§ 6. Any one of these common-terms then serves as a 
" Sign" [or Representative] of a Class ; and may be ap- 
plied to, — that is, affirmed of — all, or any, of the things 
it is thus taken to stand for. 

And you will have perceived from the above explana- 
tions, that what is expressed by a common-term is merely 
an inadequate — incomplete notion [or "view" taken] of an 
individual. For if, in thinking of some individual object, 
you retain in your mind all the circumstances (of character 
time, place, &c.,) which distinguish it (or which might dis- 
tinguish it) from others, — including the circumstance of 
unity [or singleness] — then any name by which you might j 
denote it, when thus viewed, would be a Singular-term ; I 
but if you lay aside and disregard all these circumstances, 
and abstract [consider separately] merely the points which 
are common — or which conceivably might be common — to 
it with other individuals, you may then, by taking this 
incomplete view [or, "apprehension"] of it, apply to it a 
name expressing nothing that is peculiar to it • and which 
consequently will equally well apply to each of those 
others; in short, a common-term; such as those in the 
above examples. 

§ 7. You are to remember then, that there is not in 
the case of these "general" [or common] Terms, (as there 
is in the case of Singular-terms), some real thing corres- 
ponding to each Term, existing independently of the 
Term, and of which that term is merely the name : in 
the same manner as "Lebanon" is the name of an| 
actually-existing single individual. 

At first sight, indeed, you might imagine that as anyl 
"individual man" of your acquaintance, or "Great Bri-' 
tain" or "the Sun," &c, has an existence in nature quite! 
independent of the name you call it by, so, in like manf 
ner, there must be some one real thing existing in nature! 
of which the common-term "Man" or the term " Island'! 
is merely the name. 



Lesson vii.] abstract-ideas. 47 

And some writers will tell you that this thing, which is 
the subject of your thoughts when you are employing a 
general-term, is, the "abstract-idea" of Man, of Island, of 
Mountain, &c. But you will find no one able to explain 
what sort of a thing any such " abstract idea" can be, 
which is one thing, and yet not an individual, and which 
may exist at one and the same time in the minds of several 
different person.* 

All the obscure and seemingly-profound disquisitions 
that you may perhaps meet with, respecting these sup- 
posed " abstract-ideas" will but perplex and bewilder 
you. 

Whether the writers of these disquisitions have them- 
selves understood their own meaning, we need not here 
inquire. But the simple explanation that has been above 
given of the origin and use of Common-terms, you will 
be able, with moderate attention, clearly to understand. 
And you will find it quite sufficient for our present 
purpose. 

§ 8. You will perceive from it, that the subject of our 
thoughts when we are employing a Common-term, is, the 
Term itself, regarded as a "Sign;" namely a Sign denot- 
ing a certain inadequate notion formed [or, view taken] 
of an individual which in some point agrees with [or 
" resembles"] some other individuals : the notion being, 
as has been said, " inadequate" or "incomplete," inasmuch 
as it omits all peculiarity that distinguishes the one in- 
dividual from the others; so that the same single "Sign" 
may stand equally well for any of them. 

And when several persons are all employing and under- 
standing the same Common-term in the same sense, and 
are thence said (as some writers express it) to have " one 
and the same idea" at once in the mind of each, this means 
merely that they are (thus far) all thinking alike ; just as 
several persons are said to be all "in one and the same 
posture" when they have all of them their limbs placed 

* The question here briefly alluded to, and which could not properly be 
treated of at large in a short elementary work, is that which was at one time 
fiercely contested, throughout nearly all Europe, between the two rival sects 
of Philosophers, the Realists and the Nominalists. 

There are several well-known works in which the student may find it fully 
discussed. — See Whately's Elements of Logic, B. iv. c. 5. 



48 ANALYTICAL INTRODUCTION. [Part I. 

alike; and to be of one and the same complexion when 
their skins are coloured alike. 



LESSOR VIII. 



§ 1. It has been shown, how, by taking an inadequate 
view of an individual, disregarding every point wherein 
it differs from certain other individuals, and abstracting 
that wherein it agrees with them, we can then employ a 
Common-term as a sign to express all or any of them : 
and that this process is called " generalization." 

It is plain, that the same process may be further and 
further extended, by continuing to abstract from each of 
the Classes [or Common-terms] thus formed, the circum- 
stance wherein it agrees with some others, leaving out 
and disregarding the points of difference ; and thus form- 
ing a still more general and comprehensive term. 

From an individual " Cedar," for instance, you may 
arrive in this manner at the notion expressed by the 
Common-term "Cedar," and thence again proceed to 
the more general term " Tree," and thence again to 
" Vegetable," &c. 

And so, also, you may advance from any "ten" objects 
before you,) for instance, the fingers • from which doubt- 
less arose the custom of reckoning by tens,) to the 
general term, — the number "ten;" and thence again to 
the more general term, "number;" and ultimately to the 
term ' ' quantity. ' ' 

§ 2. The faculty of Abstraction, — at least the ready 
exercise of it in the employment of Signs [Common- 
terms], seems to be the chief distinction of the Human 
Intellect from that of Brutes. These, as is well known, 
often display much intelligence of another kind, in cases 
where Instinct can have no place: especially in the 
things which have been taught to the more docile among 
domesticated animals. But the Faculty of Language, 
such as can serve for an Instrument of Reasoning, — that 
is, considered as consisting of arbitrary general Signs, — 
seems to be wanting in Brutes. 



is 



Lesson viii.] deaf-mutes. 49 

They do possess, in a certain degree, the use of Lan- 
guage considered as a mode of communication; for it 
is well known that horses, and dogs, and many other 
animals understand something of what is said to them ; 
and some brutes can learn to utter sounds indicating- 
certain feelings or perceptions. But they cannot — from 
their total want, or at least great deficiency, of the power 
of Abstraction — be taught to use language as an Instru- 
ment of Reasoning. 

Accordingly, even the most intelligent Brutes seem 
incapable of forming any distinct notion of number; to 
do which evidently depends on Abstraction. For in order 
to count any objects, you must withdraw your thoughts 
from all differences between them and regard them simply 
as units. And, accordingly, the Savage Tribes (who are 
less removed than we are from the Brutes) are remarked 
for a great deficiency in their notions of number. Few 
of them can count beyond ten, or twenty ; and some of 
the rudest Savages have no words to express any numbers 
beyond live. 

And universally, it is in all matters where the exercise 
of Abstraction is concerned, that the inferiority of Savages 
to Civilized men is the most remarkable. 

§ 3. That we do, necessarily, employ Abstraction in 
order to reason, you will perceive from the foregoing ex- 
planations and examples. For you will have observed 
that there can be no Syllogism without a Common- 
term. 

And accordingly, a Deaf-mute, before he has been taught 

a Language, — either the Finger-language, or Reading — 

cannot carry on a train of Reasoning, any more than a 

Brute. He differs indeed from a Brute in possessing the 

\"\ mental capability of employing Language ; but he can no 

'i more make use of that capability, till he is in possession 

' of some System of Arbitrary general-signs, than a person 

born blind from a Cataract can make use of his capacity 

of Seeing, till the Cataract is removed. 

You will find accordingly, if you question a Deaf-mute 
who has been taught Language after having grown up, 
that no such thing as a train of Reasoning had ever 
passed through his mind before he was taught. 



50 ANALYTICAL INTRODUCTION. [Part I. 

If indeed we did reason by means of those "Abstract- 
jdeas," which some persons talk of, and if the Language 
we used served merely to communicate with other men, 
then a person would be able to reason who had no know- 
ledge of any arbitrary Signs. But there are no grounds 
for believing that this is possible; nor, consequently, 
that "Abstract-ideas" (in that sense of the word) have 
any existence at all. 

You will have observed also, from what has been said, 
that the Signs [Common-terms] we are speaking of as 
necessary for the Reasoning-process need not be addressed 
to the ear. The signs of the numbers — the figures 1, 2, 
3, 4, <fec, — have no necessary connexion with sound; but 
are equally understood by the English, French, Dutch, 
&c., whose spo&en-languages are quite different. 

And the vjhole of the wW^m-language of the Chinese 
Is of this kind. In the different Provinces of China, they 
speak different Dialects; but all read the same characters ; 
each of which (like the figures 1, 2, 3, &c.) has a sense 
quite independent of the sound. 

And to the Deaf-mutes, it must be so with all kinds 
of Language understood by them ; whether Common 
Writing, or the Finger-language.* 



* There have been some very interesting accounts published, by travellers in 
America, and. by persons residing there, of a girl named Laura Bridgeman, who 
has been from birth, not only deaf and dumb, but also blind. She has, how- 
ever, been taught the finger language, and even to read, what is printed in 
raised characters, and also to write. 

The remarkable circumstance in reference to the present subject, is, that 
■when she is alone, her fingers are generally observed to be moving, though the 
signs are so slight and imperfect, that others cannot make out what she is 
thinking of. But if they inquire of her she will tell them. 

It seems that, having once learned the use of Signs, she finds the necessity 
of them as an Instrument of thought, when thinking of any thing beyond mere 
Individual objects of sense. 

And doubtless every one else does the same ; though in our case, no one can 
(as in the case of Laura Bridgeman) see the operation ; nor, in general can it 
"be heard; though some few persons have a habit of occasionally audibly 
talking to themselves ; or, as it is called "thinking aloud." But the Signs we 
commonly use in silent reflexion are merely mental conceptions of uttered 
words : and these, doubtless, are such, as could be hardly at all understood by 
another, even if uttered audibly. For we usually think in a kind of short-hand 
(if one may use the expression), like the notes one sometimes takes down on 
paper to help the memory, which consist of a word or two, — or even a letter, — 
to suggest a whole sentence ; so that such notes would be unintelligible to aDy 
one else. 

It has been observed also that this girl, when asleep, and doubtless dreaming, 
has her fingers frequently in motion ; being in fact talking in her sleep . 






Lesson viii.] habits of abstraction. 51 

§ 4. By the exercise of Abstraction, (it is to be farther 
remarked,) we not only can separate, and consider apart 
from the rest, some circumstance belonging to every one 
of several individuals before the mind, so as to denote 
them by a general [" common"] term, — and can also by 
repeating the process, advance to more and more general 
terms ; — but we are also able to fix, arbitrarily, on what- 
ever circumstance we choose to abstract, according to the 
particular purpose we may have in view. 

Suppose, for instance, it is some individual " Building' 7 
that we are considering : in respect of its materials we may 
refer it to the class (suppose) of " Stone-buildings," or of 
"wooden," <fec. ; in respect of its use, it may be (suppose) 
a " house," as distinguished from a Chapel, a Barn, &c; 
in respect of Orders of Architecture, it may be a " Gothic 
building," or a "Grecian," &c; in respect of size, it may 
be a "large," or a "small building;" in respect of color, 
it may be "white," "red," "brown," &c. 

And so with respect to anything else that may be the 
subject of our reasoning, on each occasion that occurs. 
We arbitrarily fix on, and abstract, out of all the things 
actually existing in the subject, that one which is impor- 
tant to the purpose in hand. So that the same thing is 
referred to one Class or to another, (of all those to which 
it really is referable,) according to the occasion. 

For instance, in the example above, you might refer 
the "building" you were speaking of, to the Class [or 
Predicable] of " white-buiLdings^ — or even of "white- 
ohjects," — if your purpose were to show that it might be 
used as a land-mark; if you were reasoning concerning 
its danger from fire, you might class it (supposing it were 
of wood) not only with such buildings, but also with hay- 
stacks and other combustibles : if the building were about 
to be sold, along with, perhaps, not only other buildings, 
but likewise cattle, land, farming implements, &c, that 
were for sale at the same time, the point you would then 
abstract, would be, its being an article of value. And so 
in other cases. 

§ 5. You must perceive clearly, that we are not to con- 
sider each object as really and properly belonging to and 
forming a portion of, some one Class only, rather than 



52 ANALYTICAL INTRODUCTION. [Part I. 

any other that may with truth be affirmed of it ; and that 
it depends on the particular train of thought we happen 
to be engaged in, ivhat it is that is important and proper 
to be noticed, and what again, is an insignificant circum- 
stance, and foreign from the question. 

But some persons who have been always engaged in 
some one pursuit or occupation, without attending to 
any other, are apt to acquire a narrow-minded habit of 
regarding almost everything in one particular point of 
view ; that is, considering each object in reference only 
to their own pursuit. 

For instance, a mere Botanist might think it some- 
thing strange aud improper, if he heard an agriculturist 
classing together, under the title of •" artificial grasses" 
such plants as Clover, Tares, and Bye-grass; which 
botanically are widely different. And the mere farmer 
might no less think it strange to hear the troublesome 
"weed" (as he has been used to call it) that is known 
by the name of "Couch-grass," ranked by the Botanist 
as a species of " wheat," the "Triticum repens," the 
farmer having been accustomed to rank it along with 
"nettles, and thistles;" with which it has no botanical 
connexion. 

Yet neither of these classifications [or "generaliza- 
tions"] would be in itself erroneous and improper: 
though it would be improper, in a Work on Natural 
History to class plants according to their agricultural uses ; 
or, in an agricultural Treatise, to consider principally (as 
the Botanist does) the structure of their flowers. 

So also, it would be quite impertinent to take into 
consideration a man's learning or ability, if the question 
were as to the allowance of food requisite for his support ; 
or his stature, if you were inquiring into his qualifications 
as a statesman ; or the amount of his property, if you 
were inquiring into his state of health ; or his muscular 
strength, if the question were as to his moral character : 
though each of these might be important in reference 
to a different inquiry. 

The great importance of attending to these points, you 
will easly perceive, by referring to the analysis of Rea- 
soning which has been above given. For as the proving 



Lesson viii.] habits of abstraction. 53 

of any Conclusion consists in referring that of which 
something is to be affirmed or denied, to a class [or 
Predicable] of which that affirmation or denial can be 
made, our ability in Reasoning must depend on our power 
of abstracting correctly, clearly, and promptly from the 
subject in question, that which may furnish a "middle- 
term " suitable to the occasion. 



54 

PART II. 
COMPENDIUM. 



LESSON IX. 



§ 1. We have gone through, in the way of a slight 
sketch, the Analysis of Reasoning. To analyse (as has 
been already explained) means to " take to pieces " so as 
to resolve anything into its elements [or component-parts.] 
Thus a Chemist is said to " analyse" any compound sub- 
stance that is before him, when he exhibits separately 
the simpler substances it is composed of, and resolves 
these again into their elements. And when, again, he 
combines these elements into their compounds, and those 
again into furthur compounds — thus reversing the former 
process, (which is called the "analytical,") he is said to be 
proceeding synthetically: the word " Synthesis" — which 
signifies "putting together," — being the opposite of 
"Analysis." 

Accordingly, it has been shown, in the foregoing 
Lessons, that every train of Argument being capable of 
being exhibited in a series of Syllogisms, a Syllogism 
contains three Propositions, and a Proposition two Terms. 
And it has been shown, how " Common-terms" (which are 
indispensable for reasoning) are obtained by means of 
Abstraction from Individual objects. 

This analytical method is the best suited for the first 
introduction of any study to a learner; because he there 
sees, from the very beginning, the practical application 
of whatever is taught. But the opposite method — the 
synthetical — is the more convenient for storing up in the 
mind all that is to be remembered. 

We shall therefore now go over a great part of the 
same ground in a reversed order, merely referring to such 
things as have been already taught, and adding such fur- 
ther rules, and explanation of additional technical-terms, 
as may be needed. 



Lesson ix.] the "dialectic-art." 55 

§ 2. The act of the mind in taking in the meaning 
of a Term, is called, in technical language, the act [or 
"operation"] of "Simple apprehension;" that is, "mere 
apprehension," [or "apprehension only."] When a pro- 
position is stated — which consists, as we have seen, of 
Wo terms, one of which is affirmed or denied of the other 
— the "operation" [or "act"] of the mind is technically 
called "Judgment." And the two terms are described 
in technical language, as "compared" together, and as 
"agreeing," or as "disagreeing," according as you affirm 
or deny, the one of the other. 

When from certain Judgments you proceed to another 
Judgment resulting from them, — that is, when you infer 
[or deduce] a Proposition from certain other Propositions 
■ — this "operation" is called "Reasoning" or "Argument- 
ation," or (in the language of some writers) "Discourse." 

And these are all the mental operations that we are at 
present concerned with. 

Each of these operations is liable to a corresponding 
defect; namely, "Simple-apprehension" to indistinctness, 
"Judgment" to falsity, and "Reasoning" to inconclusive- 
ness; [or fallaciousness.] And it is desirable to avail our- 
selves of any rules and cautions as to the employment of 
language, that may serve to guard against these defects, 
to the utmost degree that is possible : in other words, to 
guard, by the best, rules we can frame, against Terms not 
conveying a distinct meaning; — against false Propositions 
mistaken for true, — and against apparent-arguments [or 
"Fallacies" or "Sophisms"] which are in reality incon- 
clusive, though likely to be mistaken for real [valid] 
arguments. 

And such a system of Pules, * based on a scientific view 
of the Peasoning-process, and of everything connected 
with it, is what the ancient Greeks, among whom it 
originated, called the "Dialectic-art;" from a word signi- 
fying to "discourse on," or "discuss" a subject. 

§ 3. You are to observe, however, two important dis- 
tinctions in reference to the above-mentioned defects; 



* You are to observe, that a Science properly consists of general truths that 
&re to l>e known i an Art, of practical rules for something that is to he don*. 



56 compendium. [Part II. 

1st, you are to remember that which is, really, a Term, 
may be indistinctly apprehended by the person employing 
it, or by his hearer; and so also, a Proposition which is 
false, is not the less a real Proposition ; but, on the other 
hand, any expression or statement which does not 
really prove anything is not, really, an argument at all, 
though it may be brought forward and passed off as 
such. 

2ndly, it is to be remembered, that (as it is evident 
from what has been just said) no rules can be devised 
that will equally guard against all three of the above- 
mentioned defects. 

To arrive at a distinct apprehension of everything that 
may be exj)ressed by any term whatever, and again, to 
ascertain the truth or falsity of every conceivable Pro- 
position, is manifestly beyond the reach of any system 
of rules. But, on the other hand, it is possible to exhibit 
any pretended Argument whatever in such a form as 
to be able to pronounce decisively on it validity or its 
fallaciousness. 

So that the last of three defects alluded to (though not 
the two former) may be directly and completely obviated 
by the application of suitable rules. But the other two 
defects can be guarded against, (as will presently be 
shown,) only indirectly, and to a certain degree. 

In other words, rules may be framed that will enable 
us to decide what is, or is not, really a "Term," — really, 
a "Proposition," — or really an "Argument:" and to do 
this, is to guard completely against the defect of incon- 
clusiveness ; since nothing that is inconclusive is, really, 
an "Argument;" though that may be really a "Term" of 
which you do not distinctly apprehend the meaning; and 
that which is really a "Proposition" may be a false 
Proposition. 

§ 4. When two terms are brought together (or "com- 
pared," as some express it) as Subject and Predicate of a 
Proposition, they are (as was above remarked) described 
in technical language, as "agreeing," or "disagreeing," 
according as the one is affirmed or denied, of the other. 

This "agreement," however, does not (you are to ob- 
serve) mean coincidence; [or that the two terms are 



Lesson ix.] convertible terms. 57 

" equivalent ;"] for when I say "Every X is Y," or "Every 
Sheep is a ruminant-animal/' this does not mean " X is 
equivalent to Y;" [or "X" and "Y" are terms of equal 
extent;'] indeed, we know that "ruminant-animal" is in 
fact a term of greater extent than "sheep;" including 
several other species besides. We only mean to assert 
that it is a Class [or Predicable] comprehending under it, 
at least the term "Sheep;" but whether it does or does 
not comprehend anything else besides, the proposition 
before us does not declare. 

Hence it is that (as was formerly explained) the Pre- 
dicate of an Affirmative-Tproposition is considered as 
undistributed: the Subject being compared with part at 
least of the Predicate, and asserted to "agree" with it; 
but whether there be, or be not, any other part of the 
Predicate which does not agree with that subject, is not 
declared in the proposition itself. 

There are, it is to be observed, two apparent exceptions 
to this rule : 1st, the case of a Proposition which gives a 
Definition of anything : as when I say "a triangle is a three- 
sided figure;" which would not be a correct definition; 
unless it were also true that "every three-sided figure 
is a triangle ;" and 2ndly, by the case of an affirmative- 
Proposition, where both terms are singular, and denote, 
of course, one and the same Individual; as "Ishmael was 
the first-born of Abraham." 

In both these cases, the Subject and Predicate are, in 
each proposition, what are called "convertible" [or "equi- 
valent"] terms. But then, to assert or imply both that 
a certain afiirmative-proposition is true and also that its 
terms are equivalent, is to make (as was formerly remarked) 
not merely one, but two assertions. 

ISTow if I am understood to mean not only that it is true 
that "a triangle is a three-sided figure," but also that this 
is the definition of a "triangle," then, I am understood as 
making two assertions; that not only "every triangle is a 
three-sided figure," but also that "every three-sided figure 
is a triangle." But this is understood not from the Pro- 
position itself, looking to the form of expression alone, but 
from what we know, or think, respecting the sense of the 
Terms themselves, or from what we suppose the speaker 



58 compendium. [Part II. 

to have intended by those Terms. For, all that is implied 
in the mere form of an affirmative-proposition, — as "X is 
Y" — is simply that some part at least of the term "Y" 
(whatever that symbol may stand for), is pronounced to 
agree with the term "X." 

§ 5. And a like explanation will apply in the other 
ease also. If I understand from the sense of the terms in 
some affirmative-proposition, that the Subject and the 
Predicate are each a Singular-term (denoting, of course, 
one and the same individual), as "Ishmael was the first- 
born of Abraham/' then I understand, as implied by the 
meaning of the words (though not, by the form of the 
Proposition) another proposition also ; namely, that " the 
first-born of Abraham was Ishmael." In short, it is from 
my knowledge of the sense of the terms themselves that 
I understand them to be " convertible" [or equivalent J 
terms. For you may observe, that a Singular-term must 
from its own nature, correspond to a Common-term taken 
universally, [or " distributed"], inasmuch as it cannot but 
stand for the whole (not merely some part) of that which 
it denotes. 

In such cases as the above, then, that which is expressed 
as one proposition, is so understood from the meaning of 
the words as in reality to imply two. And thore is, there- 
fore, no real exception to the rule, that an Affirmative- 
proposition does not, hy the form of the expression, distribute 
its Predicate. 

§ 6. That which pronounces the agreement or disagree- 
ment of the two Terms of a Proposition [or which makes 
it affirmative or negative] is called, as has been above 
SBfeid, the " Copula." And this is always in sense, either 
*•■<,<" or "is not." For every Verb, except what is called 
tue " Substantive- verb" to "be," contains something more 
than a bare assertion of the agreement or disagreement 
of two terms. It always contains in it the Predicate (or 
part of the Predicate) also. 

Thus, the proposition "it rains" (which in Latin would 
be expressed by the single word "pluit") is resolved 

Sub. Cop. Pred. 

into "Rain — is — falling;" or in some such way. "John 

Subj. Cop. 

owes William a pound," is resolved into "John — is — ■ 



Lesson ix.] clearness of expression. 59 

Pred. 

owing [or indebted to] William a Pound." And so in 
all such cases. 

Sometimes, indeed, even the substantive- verb itself is 
both Copula and Predicate ; namely, where existence alone 
is affirmed or denied; as "God is;" "one of Jacob's sons 
is not";* in which cases "existing" is the Predicate. 

You are to observe, that the Copula has in itself no 
relation to time. If, therefore, any other tense besides 
the Present, of the Substantive-verb, is used, it is to be 
understood as the same in sense with the Present, as far 
as the assertion is concerned ; the difference of tense 
being regarded (as well as the person and number) 
merely as a matter of grammatical propriety : unless it 
be where the circumstance of time really does affect the 
sense of the proposition. And then this circumstance is 
to be regarded as part of one of the Terms; as, "this 
man was honest;" that is, "he is oris formerly -honest" 
In such a case, an emphasis, with a peculiar tone, is laid 
on the word "was." 

An infinitive, you are to observe, is not a Verb (since 
it can contain no affirmation or denial), but a verbal 
noun-substantive. And a Participle, again, is a verbal 
adjective. 

A Participle, or any other Adjective, may be made a 
Predicate, but not (by itself) a subject of a proposition; 
as "this grass is green," "that grass is mown." 

An infinitive, though generally placed (in English) at 
the end of a sentence, is almost always (when it is by 
itself a Term) the Subject; as "I like to ride;" that is, 

Sub. Pred. 

"To ride, [or "riding"] is — a thing I like." 

And observe that there is, in English, an infinitive in 
" ing," the same in sound with the Participle, but different 
in sense. When I say "Hiding" [or "to ride"] "is plea- 
sant," and again "that man is riding," in the former 
sentence the word "riding" is a Substantive, and is the 
Subject ; in the latter it is an adjective [Participle] and 
is the Predicate. 

* Gen. xlii. 13. 



60 compendium. [Part II. 

One infinitive, however, is sometimes predicated of 
another infinitive: as, " seeing is believing;" "not to 
advance is to fall back;" "to be born is not to be per- 
fected." 

§ 7. A term may consist (as was formerly explained) of 
one word, or of several. And care must be taken, when 
you are examining a proposition, not to mistake for one of 
its Terms a word which, though it might have been used 
as a Term, is, in that proposition, only a part of a Term. 
Thus, in one of the above examples, the word "pound" is 
not one of the Terms, but only a part of the Term "owing 
a pound to William." A description of some object will 
sometimes occupy a page or two, and yet be only the 
Predicate of a single Proposition. 

You are to observe, also, that one single sentence will 
often imply what may be regarded as several distinct 
Propositions ; each, indeed, implying the truth of the 
others, but having their terms different, according as we 
understand the drift (as it is called) or design of what 
is uttered: that is, according to what we understand the 
person to be speaking of (which is the subject), and what 
it is that he says [predicates] of it. 

1 2 3 4 

Thus "He — did not — design — your — death" — may be 
regarded as any one of at least four different proposi- 
tions. If (No. 1.), the word "He" be marked by emphasis 
in speaking, or by italics, it will be understood as the 
Predicate ; and the drift of the sentence will be, that 
"whoever else may have designed your death, it was not 
He:' 1 if the emphasis fall on No. 2, the Predicate will 
be "designing," [or by "design"], and the drift of the 
sentence will be, that " though he may have endangered 
your life, it was not by design: 1 and so with the rest. 

You should endeavour, therefore, so to express your- 
self, as to make it clearly understood not only what is the 
meaning of each word you employ, but also what is the 
general drift of the whole sentence ; in short, what is 
the Subject of your Proposition, and what it is that you 
say of it. And as far as you can, you should make this 
clear by the structure of each sentence, without resorting 
to the expedient of italics or under-scoring oftener than 
is unavoidable. 



Lesson x.] proposition. 61 

There is frequently a great advantage towards such 
clearness, gained by the English word "it" in that sense 
in which it stands (not as the neuter pronoun, answering 
to "He" and "She," but) as the representative of the Subject 
of a Proposition, of whatever Gender or number ; so as 
to allow the subject itself to be placed last : as — 

Subj. Cop. Pred. Subj. 

"It — is not — he — that had this design;" 
Or again — 

Subj. Cop. Pred. Subj. 

" It — is not — by design — that he did this," &c. 



LESSON X. 



§ 1. A Proposition is, as has been said, an act of judg- 
ment expressed in words; and is defined to be a " Sentence 
which asserts;" or, in the language of some writers, an 
"indicative Sentence:" "indicative" [or "asserting,"] 
meaning "that which affirms or denies something." It 
is this that distinguishes a Proposition from a Question, 
or a Command, &c. 

Propositions considered merely as Sentences, are distin- 
guished into "Categorical" and " Hypothetical." 

The Categorical asserts simply, that the Predicate 
does, or does not, apply to the Subject: as "the world 
had an intelligent Maker:" "Man is not capable of rais- 
ing himself, unassisted, from the savage to the civilized 
state." The Hypothetical [called by some writers, "Com- 
pound"] makes its assertion under a Condition, or with 
an Alternative; as "if the World is not the work of chance, 
it must have had an intelligent Maker:" "Either man- 
kind are capable of rising into civilization unassisted, or the 
first beginning of civilization must have come from above." 

The former of these two last examples is of that kind 
called "Conditional-proposition;"* the u condition" being 
denoted by "if," or some such word. The latter example 
is of the kind called "Disjunctive;" the alternative being 
denoted by "either" and "or." 

• Or, "hypothetical" according to those writers who use the word "com- 
pound" when we have used "hypothetical." 



62 compendium. [Part II. 

The division of Propositions into Categorical and 
Hypothetical, is, as has been said, a division of them con- 
sidered merely as Sentences; for a light distinction might 
be extended to other kinds of Sentences also. Thus 
"Are men capable of raising themselves to civilization V 
"Go and study books of travels," are what might be 
called categorical sentences, though not propositions. " If 
man is incapable of civilizing himself, whence came the 
first beginning of civilization]" might be considered as a 
conditional question; and "Either admit the conclusion, 
or refute the argument," is a disjunctive command. 

At present we shall treat only of Categorical Proposi- 
tions. 

§ 2. It has been above explained, that Propositions (of 
this Class, — the Categorical) are divided according to 
their "Quantity" into "Universal" and "Particular;" — 
that an "/nc?e/z rate-proposition" is in reality either the 
one or the other; though the form of expression does not 
declare which is meant: — and also that a " Singular '-pro- 
position is equivalent to "Universal," since its subject 
cannot but stand for the whole of what that Term 
denotes, when that whole is one single individual. 

You have also learnt that propositions are divided, 
according to their "Quality," into "affirmative" and "ne- 
gative." The division of them, again, into "true" and 
"false" is also called a division according to their 
"quality;" namely, the "quality of Matter)' (as it has 
relation to the subject-matter one is treating of;) while 
the other kind of quality (a proposition's being affirmative 
or negative) is "the quality of the expression." 

The "quality of the matter" is considered (in relation 
to our present inquiries) as accidental, and the "quality of 
the ex]3ression" as essential. For though the truth or 
falsity of a proposition — for instance, in Natural-history, 
is the most essential point in reference to Natural-history ', 
and of a mathematical proposition in reference to Mathe- 
matics, and so in other cases, — this is merely accidental in 
reference to an inquiry (such as the present) only as 
to forms of expression. In reference to that, the essential 
difference is that between affirmation and negation. 

And here it should be remarked by the way, that as 



LeSSOIl x.] CATEGOKXCAt, PROPOSITIONS, 63 

on the one hand, ev<lry Proposition must be either true or 
false, so, on the other hand, nothing else can be, strictly 
Speaking;, either true or false. In colloquial language, 
however^ "true" and "false" are often more loosely 
applied; as when men speak of the "true cause" of any- 
thing; meaning "the real cause/' — the "true heir," that 
is, the rightful heir; — =a "false prophet,"— that is, a pre- 
tended prophet, or one who utters falsehoods; — a "true" 
or "false" argument, meaning a valid [real], or an appa- 
re^-argument— a man "true" or "false" to his friend; 
i. e., faithful, or unfaithful, &o. 

A Proposition, you are to observe, is Affirmative or 
Negative, according to its Copida; i. e., according as the 
Predicate is affirmed or denied of the Subject, Thus, 
"not to advance, is to fall back," is affirmative; "No 
miser is truly rich" [or " a miser is not truly rich"] is a 
negative. "A few of the sailors were saved," is an affir- 
mative ; " Few of the sailors were saved," is properly 
a negative: for it would be understood that you wero 
speaking of "most of the sailors" and denying that they 
were saved. 

Since then every Proposition must be either Affirmative 
or Negative, and also, either Universal or Particular, 
Propositions are considered as divided (taking into 
account both Quantity and Quality) into four Classes* 
which, for brevity's sake, are usually denoted by the 
Symbols A, E, I, O; namely A, Universal-affirmative, 
E, Universal-negative, I, Particular-affirmative, and > 
Particular-negative. 

§ 3. Any two Propositions are, technically, said to bo 
" opposed" 1 ' to each other, when, " having the same Subject 
and Predicate, they differ either in Quantity or in Quality,, 

i Or in both." 

In ordinary language, however, (and in some technical 

! treatises) propositions are not to be reckoned as " opposed" 

I unless they differ in Quality. 

It is evident that with any given Subject and Predicate^ 
you may state four distinct Propositions, A, E, I, and O ; 
any two of which are said to be " opposed." And hence 
there are (in the language of most technical writers} 
reckoned four kinds of "Opposition." 1st, A and E,— 



64 



COMPENDIUM. 



[Part II. 



the two TTniversals, Affirmative and Negative, (always 
supposing the Terms the same) are called "Contraries" 
to each other: 2nd, The Two Particulars, I and O, "Sub- 
contraries." 3rd, The Two Affirmatives again, or the two 
Negatives, (A and I, or again, E and 0,) are called " Sub- 
alterns;" and 4th, those which differ both in Quantity 
and Quality — as A and 0, or E and I, — are called Con- 
tradictories" 

It is usual to exhibit in a Scheme (such as that below) 
these four kinds of " Opposition;" by placing at the 
corners of a Square the Symbols A, E, I, O, as represen- 
ting, respectively, the above-mentioned four classes of 
Propositions. 

n. t A - - - - Contraries - - — — E n./. 

i. /. [Every X is Y.] [No X is Y.] i. t 

c./. c./. 



V ^ 



c°" 



<& 



f $> 



*, 



W 



n.t. 
c. t. 



[Some X is Y.] 



Sub contraries 



- - - 

[Some X is not Y.] 



n./. 
i. t. 
c. t. 



You may substitute for the unmeaning Symbols, X, Y, 
(which stand for the Terms of the above Propositions) 
whatever significant Terms you will ; and on their mean- 
ing, of course, will depend the truth or falsity of each 
Proposition. 

For instance, Naturalists have observed, that "animals 
having horns on the head are universally ruminant ;" that, 
of "carnivorous animals' ; none are ruminant; and that 



Lesson x.] opposition. 65 

of " animals with hoofs," some are ruminant, and some 
not. Let us take then instead of "X," "animals with 
horns on the head/' and for " Y," "ruminant :" here, the 
real connection of the Terms in respect of their meaning — 
which connection is called the "matter" of a proposition — 
is such that the Predicate may be affirmed universally of 
the subject; and of course the affirmatives (whether Uni- 
versal or Particular) will be true, and the "negatives" 
false. In this case, the "matter" is technically called 
"necessary," inasmuch as we cannot avoid believing the 
Predicate to be applicable to the Subject. 

Again let "X" represent "carnivorous animal," and 
" Y" "ruminant;" this is a case of what is called "impos- 
sible matter;" (i.e. where we cannot believe it possible for 
the Predicate to be applicable to the Subject) being just 
the reverse of the foregoing; and, of course, both the 
Affirmatives will here be false, and both negatives true. 

And lastly, as an instance of what is called "contingent 
matter," i.e. where the Predicate can neither be affirmed 
universally, nor denied universally, of the Subject, take 
"hoofed animal" for "X" and "ruminant" for "Y;" 
and of course the universals will both be false, and the 
Particulars, true: that is, it is equally true, that "some 
hoofed animals are ruminant," and that " some are not." 

§ 4. You will perceive then, on examining such a 
Scheme, that "contrary" Propositions can never be both 
of them true, though they may (viz. : in "contingent-mat- 
ter") be both false : that " $w&-contraries," on the other 
hand, may be both true, but never both false: that " Con- 
tradictories" \diametrically-oipposite Propositions] must in 
in every case be, one true, and the other false : and that 
"Subalterns" (of which the Universal is called the " Sub- 
alterram//' and the Particular " Subaltemafe") may be 
either both true, or both false, or the one true and the 
other false. 

These last propositions, however, though reckoned, as 
has been said above, by most dialectical writers, among 
those opposed, are not so accounted in ordinary discourse. 

The four kinds of Propositions, A, E, I, O, have been 

i in the Scheme, marked, each, with the letters t for "true" 

and f for " false," and also with the letters n, i, c, to 



§§ compendium. [Part II. 

denote the three kinds of matter, (necessary, impossible, 
contingent), in order to point out whieh propositions are 
true, and which false, in each kind of matter. 

The technical terms we have here explained, are need- 
ful to be learnt, as being some of them in frequent use, 
and as being convenient for the avoiding of circumlocution 
and of indistinctness. 

" Contradictoiy-opposition" is the kind most frequently 
alluded to, because (as is evident from what has been just 
said) to deny, — or to disbelieve — a proposition, is to assert 
or to believe, its Contradictory; and of course, to assent 
to, or maintain a proposition, is to reject its Contradictory. 
Belief, therefore, and Disbelief are not two different states 
of the mind, but the same, only considered in reference to 
two Contradictory propositions. And consequently Cre- 
dulity and Incredulity are not opposite habits, but the 
same; in reference to some class of propositions, and to 
their contradictories.* 

For instance, he who is the most incredulous respecting 
a certain person's guilt, is, in other words, the most ready 
to believe him not guilty ; he who is the most credulousf 
as to certain works being within the reach of Magic is 
the most incredulous [or "slow of heart to believe' '] that 
they are not within the reach of Magic; and so in all 
cases. 

The reverse of believing this or that individual proposi- 
tion, is, no doubt, to disbelieve that same proposition : but 
the reverse of belief generally, is (not disbelief; since that 
implies belief; but) doubt. 

And there may even be cases in which doubt itselt 
may amount to the most extravagant credulity. For in- 
stance, if any one should "doubt whether there is any 
such Country as Egypt," he would be- in fact believing 
this most incredible proposition; that "it is possible for 
many thousands of persons, unconnected with each other, 
to have agreed, for successive Ages, in bearing witness to 

* The word "credulity" is sometimes understood as limited to the sense 
of overhasty belief in testimony. But there seems no objection to its being 
•employed, generally, to signify " hasty belief, on insufficient grounds, of what- 
ever kind." To all practical purposes, at least, this may be regarded as 
credulity. 

t As the Jews, in the time of Jesus, in respect of his works. 



Lesson x.] simple-conversion. 67 

the existence of a fictitious Country, without being de- 
tected, contradicted, or suspected." 

All this, though self-evident, is, in practice, frequently 
lost sight of. 

§ 5. A Proposition is said to be " converted" when its 
" Terms are transposed ;" i. e., when the Subject is made 
the Predicate, and the Predicate the Subject. And when 
no other change is made, this is called " simple-conversion." 
"When, for instance, I say, "no carnivorous animal" is a 
"ruminant/' the " simple-converse" of this would be, "no 
ruminant is a carnivorous animal." 

The " conversion' } of such a proposition as this, "No 
one [is happy who] is anxious for a change," would be 
effected by altering the arrangement of the words in 
brackets, into "who is happy." 

The Conversion of a Proposition is said to be "illative" 
when the truth of the "Converse" is implied (looking 
merely to the form of expression) " by the truth of the 
original proposition;" [or " eteposita;"] which is the case 
in the example above : it being evident that if the former 
of those Propositions (whatever may be the meaning of 
the Terms) be true, the Converse must be true also. For 
to say that " No X is Y," is to imply that " no Y is X." 

You are to observe, however, that the Converse of a 
true Proposition may happen to be true also, without 
the Conversion's being "illative;" that is, when the truth 
of that Converse is not implied by the truth of the " Ex- 
posita" [the original proposition]. Thus, " Every X is 
Y" does not imply that "every Y is X," though it may 
happen that both propositions may be true. 

For instance, that "Every tree is a vegetable," does not 
imply that "every vegetable is a tree;" and this last hap- 
pens in fact to be not true. But no more is it implied, 
when I say, " every equilateral triangle is equiangular," 
that "every equiangular triangle is equilateral :" for though 
both these propositions are true, the one of them does 
not imply the other; and they are separately demonstrated 
as distinct propositions, in geometrical treatises. 

In order to understand why the simple-conversion of 
"every X is Y," into "every Y is X," is not "illative/' 
you have only to observe, that, in the "Exposita," 



68 compendium. [Part II. 

[original proposition,] "Y" is undistributed, as being the 
predicate of an Affirmative; while, in the " Converse," 
it is u distributed," by being made the Subject of a Uni- 
versal. A new Term is therefore, in fact, introduced ; 
since instead of 'part of the Term " Y" we have employed 
the whole of it; and the agreement or disagreement of 
one Term with some part of another Term, does not imply 
its agreement or disagreement with every part of it; that 
is, with the whole. For though a part is implied by a 
whole, a whole is not implied by a part. 

When for instance, I say, "every tree is a vegetable,'* 
I am employing (as was formerly explained) the term 
"vegetable" to stand only for part of its " significates;" 
and this does not authorize me to employ it (in the Con- 
verse) as standing for all its Significates; as in saying 
that " every vegetable is a tree." 

And strictly speaking, that is not a real " conversion/' 
— but only an " a^arew£-conversion" — which is not "illa- 
tive." For, (as has been above said,) there is not a mere 
transposition of the terms, but a new term introduced, 
when a term which was undistributed in the "Exposita," 
is distributed [taken universally] in the Converse. 

But as it is usual, in common discourse, to speak of 
"an unsound argument," meaning "an apparent-argument, 
which is in reality not an argument/' so, in this case also, 
it is common to say, for instance, that " Euclid proves 
first that all equilateral triangles are equiangular, and 
afterwards he proves the Converse, that all equiangular 
triangles are equilateral:" or again, to say, " It is true 
that all money is wealth;" but I deny the Converse (in 
reality, the appare?it-c<m.veYse) that all wealth is money. 

§ 6 Conversion then, strictly so called, — that is, " illa- 
tive-conversion," — can only take place when no term is 
distributed in the Converse, which was undistributed in 
the "Exposita." 

Hence, since E [Universal-negative] distributes both 
terms, and I [a Particular-affirmative] neither, these may 
both be simply-converted illatively. As in the example 
above, "no carnivorous animal is ruminant," implies by 
the very form of the expression, " that no ruminant is a 
carnivorous animal." And so also, " some things which 



Lesson x.] illative-conversion. 69 

are strange are believed," implies that, "some things 
which are believed are strange." 

We may also illatively-convert A [a Universal-affirma- 
tive] by altering its "Quantity" fiom Universal to Parti- 
cular. For every " X is Y" does not imply that "some 
Y" (though not that "every Y") "is X." So, in the 
example above, we might allowably have stated (though 
not that "all vegetables," yet) that "some vegetables are 
trees." 

This procedure is called " conversion by limitation;" or 
according to some writers, "conversion per accidens." 
And it may be applied to E also; as for instance in the 
example above, you might have said " Some ruminant is 
not carnivorous;" though this would have been to come 
short of what you were warranted in stating. 

But in O [particular-negative] the conversion will not 
be illative, on account of the rule that the Predicate of a 
Negative is always distributed. The proposition therefore 
p Some X is not Y" does not imply that " some Y is not 
X;" since X is distributed in the "Converse" and was not 
in the "Exposita," in which it was the Subject of a Parti- 
cular. It is true that "some men are not negroes:" but 
this does not imply that "some negroes are not men." 

A particular-negative [O] cannot be converted illatively 
except by changing its Quality from negative to affirma- 
tive (without altering the sense), by regarding the negation 
as attached to the Predicate instead of to the Copula. 

S Cop Pr 

= Thus. "Some X is not Y," may be taken as an 

S Cop. Pr. 

i affirmative, namely, "Some X is not Y;" and this 

latter proposition [I] may of course be simply-converted 

S " Cop. Pr. 

lillatively; as " Some not Y is X." 

Thus, "Some men are not-negroes," implies that "Some 
>who are not negroes are men;" or (as such a proposition 
is often expressed) " one may be a man without being a 
megro." So again " Some who possess wealth are not 
happy," implies that " Some who are not-happy possess 
wealth. 

§ 7. This procedure is technically called " Conversion- 
hj-negation" [or, by " Contraposition"]. It is applicable 



70 compendium [Part II. 

also to [A] Universal-ainrmatives. For, to affirm some 
Predicable of a Subject, or [to assert the pn*esence of some 
attribute] is the same thing in sense as to deny its absence. 
Hence a Universal-affirmative may be stated as a Univer- 
sal-negative ; which (as we have seen) may be simply- 
converted. 

Thus " Every X is Y" is equipollent [or equivalent in 
sense] to " No X is not Y;" which may be illatively con- 
verted into " nothing that is not Y — is — X:" [or " what- 
ever is not Y- is not — X"]. 

So the proposition, " Every true poet is a man of genius," 
may be stated as "No true poet is — not-a-man-of-genius;" 
which (being E) may be illatively converted into "no one I 
who is not a man of genius is a true poet:" (as such a pro- ] 
position is very commonly expressed) "None but a man 
of genius can be a true poet;" or again, "a man of genius 
alone can be a true poet;" or again, "One cannot be a 
true poet without being a man of genuis." 

And here it is worth remarking by the way, that in I 
such examples as the above, the words a may," "can," "can- 
not," <fec, have no reference (as they sometimes have) to I 
power, as exercised by an agent; but merely to the distri- 
but ion or non-distribution of Terms; or to the confidence I 
or doubtfulness we feel respecting some supposition. 

To say, for instance, that "a man who has the plague 
may recover, does not mean that " it is in his power to 
recover if he chooses;" but it is only a form of stating a 
particular proposition-. [I] namely, that "Some who have 
the plague recover." And again, to say "there may be a 
bed of coal in this district," means merely, " The existence 
of a bed of coal in this district — is — a thing which I can- 
not confidently deny or affirm." 

§ 8. So also to say " a virtuous man cannot betray his 
Country" [or "it is impossible that a virtuous man should 
betray," &c.] does not mean that he lacks the power, (for 
there is no virtue in not doing what is out of one's power,) 
but merely that " not betraying one's country" forms an 
essential part of the notion conveyed by the term "virtu- 
ous." We mean, in short, that it is as much out of our 
power to conceive a virtuous man who should be a traitor, 
as to conceive " a Square with unequal sides;' 1 that is, a 



Lesson xi.] an argument defined. 71 

square which is not a square. The expression therefore 
is merely a way of stating the Universal-proposition [E], 
"No virtuous man betrays his Country." 

So again, to say U A weary traveller in the deserts of 
Arabia must eagerly drink when he comes to a Spring," 
does not mean that he is compelled to drink, but that / 
cannot avoid believing that he will ; — that there is no 
doubt in my mind. 

In these and many other such instances, the words 
"may," "must," "can," "impossible," &c, have reference, 
not to power or absence of power in an agent, but only to 
universality or absence of Universality in the expression; 
or, to doubt or absence of doubt in our own mind, respect- 
ing what is asserted. 



i 



LESSON XI. 



§ 1. An Argument [or Act of Reasoning expressed in 
words] is defined " an Expression in which, from some- 
thing laid down [assumed as true] something else is 
concluded to be true, as following necessarily [resulting] 
from the other." That which follows from the other, 
is called (as was formerly explained) the "Conclusion;" 
and that from which it follows, the "Premises;" or in the 
language of some writers, the "Antecedent." 

The above is the strict technical definition. But in 
ordinary language the word "Argument" is often em- 
ployed to denote the Premises alone; or, sometimes that 
one of the Premises which is expressed, when the other 
is understood : as when one speaks of proving so and so 
by this or that argument; meaning, by such and such a 
rPremise. 

And you may observe, by the way, that of the two 
:Premises, the Major (formerly explained), is in common 
discourse often called the "Principle," and the minor- 
premise the "Reason." 

Frequently also in common discourse "an Argument" 
is used to signify a " Series of arguments," leading ulti- 
mately to the Conclusion maintained. 



72 compendium. [Part II. 

An Argument, if stated in such a regular form that "its 
conclusiveness [its being really an Argument] is apparent 
from the mere form of expression alone" (independently of 
the meaning of the words,) is then called a " Syllogism." 
As, " Every X is Y ;* Z is X, and therefore Z is Y ;" in 
which, as was formerly explained, the truth of the Con- 
clusion, assuming the Premises to be true, — must be 
admitted, whatever terms you may make X, Y, and Z, 
respectively, stand for. 

You are to remember, therefore, that a Syllogism is not 
(as some have imagined) a peculiar kind of Argument ; 
but only a certain form in which every Argument may 
be exhibited. 

§ 2. One circumstance which has tended to mislead 
persons as to this point, is, that in a Syllogism we see 
the conclusion following certainly [or necessarily^ from the 
Premises; and again, in any apparent-syllogism which on 
examination is found to be (as you have seen in some of 
the examples) not a realoiiQ [not " valid"] the Conclusion 
does not follow at all ; and the whole is a mere deception. 
And yet we often hear of Arguments which have some 
weight, and yet are not quite decisive ; — of Conclusions 
which are rendered probable, but not absolutely certain, &c. 
And hence some are apt to imagine that the conclusiveness 
of an Argument admits of degrees ; and that sometimes 
a conclusion may, probably and partially, — though not 
certainly and completely — follow from its Premises. 

This mistake arises from men's forgetting that the 
Premises themselves will very often be doubtful; and, 
then, the Conclusion also will be doubtful. 

As was shown formerly, one or both of the Premises 
of a perfectly valid Syllogism may be utterly false and 
absurd : and then, the Conclusion, though inevitably 
following from them, may be either true or false, we 
cannot tell which. And if one or both of the Premises 
be merely probable, we can infer from them only a pro- 
bable conclusion ; though the conclusiveness, — that is, the 
connection between the Premises and the Conclusion — is 
perfectly certain. 

* See above. Lesson IX. § 4. 






Lesson xi.] an argument defined. 73 

For instance, assuming that "every month has 30 
days" (which is palpably false) then, from the minor- 
premise that " April is a month," it follows (which 
happens to be true) that " April has 30 days :" and from 
the minor-premise that "February is a month," it follows 
that "February has 30 days;" which is false. In each case 
the conclusiveness of the Argument is the same; but in 
every case, when we have ascertained the falsity of one 
of the Premises, we know nothing (as far as tJiat argument 
is concerned) of the truth or falsity of the Conclusion. 

§ 3. When, however, we are satisfied of the falsity of 
some Conclusion, we may, of course, be sure that (at least) 
one of the Premises is false \ since if they had both been 
true, the Conclusion would have been true. 

And this — which is called the " indirect'' 1 mode of proof 
— is often employed (even in Mathematics) for establishing 
what we maintain : that is, we prove the falsity of some 
Proposition (in other words, the truth of its contradictory) 
by showing that if assumed, as a Premise, along with 
another Premise known to be true, it leads to a Conclu- 
sion manifestly false. For though from a false assumption, 
either falsehood or truth may follow, from a true assump- 
tion, truth only can follow. 

Let us now look to the case of a doubtful Premise. 
Suppose it admitted as certain that "a murderer deserves 
death," and as probable that " this man is a murderer," 
then, the Conclusion (that "he deserves death") is pro- 
bable in exactly the same degree. 

But though when one Premise is certain, and the other 
only probable, it is evident that the Conclusion will be 
exactly as probable as the doubtful premise, there is some 
liability to mistake, in cases where each Premise is merely 
probable. For though almost every one would perceive 
that in this case the probability of the Conclusion must 
be less than that of either Premise, the precise degree in 
which its probability is diminished, is not always so 
readily apprehended. 

And yet this is a matter of exact and easy arithmetical 
calculation. I mean, that, given the probability of each 
Premise, we can readily calculate, and with perfect exact- 
ness, the probability of the Conclusion. 



74 compendium. [Part II. 

As for the probability of the Premises themselves that 
are put before us, that, of course, must depend on our 
knowledge of the subject-matter to which they relate. But 
supposing it agreed what the amount of probability is in 
each Premise, then we have only to state that probability 
in the form of & fraction, and to multiply the two fractions 
together, the product of which will give the degree of pro- 
bability of the Conclusion.* 

§ 4. Let the probability, for instance, of each Premise, 
be supposed the same; and let it in each, be§; [that is, 
let each Premise be supposed to have two to one in its 
favour; that is, to be twice as likely to be true as to be 
false ;] then the probability of the Conclusion will be two- 
thirds of two thirds; that is, |; — rather less than one-half. 
For since twice two are four, and thrice three, nine, the 
fraction expressing the probability of the Conclusion will 
be four-ninths. 

For example, suppose the Syllogism to be " A man who 
has the plague will die of it" (probably); "this man has 
the plague" (probably); therefore (probably) "he will die 
of it." We are — suppose — not certain of either Premise; 
though we think each to be probable : we have judged — 
suppose — that of 9 persons with the symptoms this man 
exhibits, two-thirds, — that is, six, have the plague : and 
again, that two-thirds of those who have the plague — that 
is, four out of six — die of it: then, of 9 persons who have 
these symptoms, 4 may be expected to die of the plague. 

Again "Every X is Y (|); Z is X (f ); therefore Z is Y 
T \— i) ; let the fractions written after each Premise ex- 
press the degree of its probability : and the result will be 
that which is given as the probability of the Conclusion. 

For instance, "A Planet without any atmosphere is un- 
inhabited: the moon is a planet without any atmosphere; 
therefore the moon is uninhabited:" supposing these Pro- 
positions to be those represented in the former example 
(of X, Y, and Z) then the probability that " the moon is 

Those who are at all familiar with Arithmetic will hardly need to be reminded 
that, — since a fraction is less than a unit, — what is called (not strictly, but 
figuratively) multiplying anything by a fraction, means taking it less than once; 
ao that for instance, JXs that is, a half multiplied (as id called) by two-thirds, 
means, two -thirds of a half ; i. t. or $. 



Lesson xi.] degrees of probability 75 

un in habited," will be two-thirds of three-fourths; or one- 
half, since J- multiplied by three-fourths gives 1 \=ly* 

In the example just given, you will observe, that the 
probability of each Premise has been supposed more than 
|- ; that is, each has been assumed to be more likely to be 
true than not ; and yet there is, for one of these Conclu- 
sions, only an even chance ; and for the other less. The 
supposed patient is supposed to be rather less likely to 
die of the plague than not. 

And, of course, when there is a long train of reasoning, 
— the conclusion of each argument being made one of 
the Premises of a succeeding one, — then, if a number of 
merely-probable Premises are introduced, the degree of 
probability diminishes at each successive stage. 

And hence it may happen, in the case of a very long 
train of reasoning, that there may be but a slight proba- 
bility for the ultimate Conclusion, even though the Pre- 
mises successively introduced should be, some of them, 
quite certain, and the rest more probable than not. 

And hence, we often have to employ several distinct 
trains of argument, each tending separately to establish 
some degree of probability in the Conclusion. 

§ 5. When you have two (or more) distinct arguments, 
each, separately, establishing as probable the same con- 
clusion, the mode of proceeding to compute the total pro- 
bability, is the reverse of that mentioned just above. For, 
there — in the case of two probable premises, — we consider 
what is the probability of their being both true; which is 
requisite, in order that the conclusion may be established 
by them. But, in the case of a conclusion twice (or offcener) 

* Some persons profess contempt for all such calculations, on the ground 
that we cannot be quite sure of the exact degree of probability of each Premise. 
And it is true, that we are, in most cases, exposed to this unavoidable course 
of uncertainty ; but this is no reason why we should not endeavour to guard 
against an additional uncertainty, which can be avoided. It is some advantage 
to have no more doubt as to the degree of probability of the Conclusion, than 
we have in respect to the Premises. 

And in fact there are offices, kept by persons whose buisness it is, in which 
calculations of this nature are made, in the purchase of contingent-reversions, 
depending, sometimes, on a great variety of risks which can only be conjectu- 
rally estimated ; and in effecting Insurances, not only against ordinary risks 
" (the calculations of which are to be drawn from statistical-tables), but also 
against every variety and degree o e.r/ra-ordinary risks ; the exact amount of 
which no one can confidently pronounce upon. But the calculations are based 
on the best estimate that can be formed. 



76 compendium. [Part II. 

proved probable by separate arguments, if these distinct 
indications of truth do not all of them fail, the conclusion 
is established. You consider, therefore, what is the pro- 
bability of both these indications of truth being combined 
in favour of any conclusion that is not true. 

Hence the mode of computation is, to state (as a frac- 
tion) the chances against the conclusion as proved by each 
argument ; and to multiply these fractions together, to 
ascertain the chances against the conclusion as resting 
on both the arguments combined; and this fraction being 
subtracted from unity, the remainder will be the proba- 
bility for the conclusion. 

For instance, let the probability of a conclusion as 
established by a certain argument, be § : (suppose that this 
man is the perpetrator of a certain murder, from stains 
of blood being found on his clothes:) and again of the 
same conclusion as established by another argument, f : 
(suppose from the testimony of some witness of somewhat 
doubtful character:) then, the chances against the conclu- 
sion in each case, respectively, will be f and §; which, 
multiplied together, give £§ or ^ against the conclusion. 
The probability, therefore, for the conclusion as depending 
on these two arguments jointly (i. e. that he is guilty of 
the murder) will be §, or two to one.* 

As for the degree of probability of each Premise, that, 
as we have said, must depend on the subject-matter before 
us; and it would be manifestly impossible to lay down any 
fixed rules for judging of this. But it would be absurd to 
complain of the want of rules for determining a point for 
which it is plain no precise rules can be given; or to dis- 
parage, for that reason, such rules as can be given for the 
determining of another point. Mathematical Science will 
enable us — given, one side of a triangle and the adjacent 
angles, — to ascertain the other sides ; and this is acknow- 
ledged to be something worth learning, although mathe- 
matics will not enable us to answer the question which is 
sometimes proposed in jest, " How long is a rope 1 ?" 

Men are often misled in practice by not attending to 
these circumstances, plain as they are, when pointed out. 

* See Lesson XVII., § 10. 



Lesson xi.] principle of reasoning. 77 

§ 6. It has been already explained that the Maxim [or 
Dictum] applicable to every Argument when stated in the 
clearest form, is, that whatever is predicated universally 
of any term-may be predicated in like manner [affirmed 
or denied, as the case may be] of whatever is compre- 
hended under that term; and that this, consequently, is 
the " Universal principle of Reasoning." 

And you may observe, that this Dictum [or Maxim] 
may, in fact, be regarded as merely the most general 
statement of "An Argument" — not this or that indivi- 
dual argument ; but any and every " Argument abstract- 
edly." 

For instance, if you say " This man is contemptible be- 
cause he is a liar," you evidently mean to be understood, 
" Every liar is contemptible; this man is a liar; therefore 
he is contemptible." Now, if you so far generalise this 
Syllogism, as to omit all consideration of the very terms 
actually occurring in it, abstracting, and attending solely 
to the form of expression, you will have " Every X is Y; 
Z is X; therefore Z is Y;" and then if you proceed 
to make a still further abstraction, saying — instead of 
"Every X" — "any-term-distributed" and instead of " Y" 
— "anything whatever affirmed of that term," and so on, 
you will have, in substance, the very " Dictum" we have 
been speaking of: which may be separated into three 
portions, corresponding to the three Propositions of a 
Syllogism; thus, — 

1. Anything whatever (as "Y") affirmed of a whole 
(as "X"). 

2. under which class something else (as "Z") is com- 
prehended. 

3. may be affirmed of that (namely "Z") which is so 
comprehended. 

These three portions, into which the Dictum has been 
separated, evidently answer to the Major-premise, Minor- 
premise, and Conclusion, of the Syllogism given above. 
And it is plain, that the like explanation will apply (if 
"denied" were put for "affirmed") to a Syllogism with a 
negative conclusion. So that the "Dictum" is in fact, as 
we have said, merely the most abstract and general form 
of stating the Act of Reasoning, universally. 



78 compendium. [Part II. 

§ 7. Some persons have remarked of this "Dictum" 
(meaning it as a disparagement) that it is merely a some- 
what circuitous explanation of ivhat is meant by a Class. 
It is in truth, just such an explanation of this as is need- 
ful to the student, and which must be kept before his mind 
in reasoning. For you are to recollect that not only every 
class [the Sign of which is, a " Common-term,"] compre- 
hends under it an indefinite number of individuals — and 
often of other Classes — differing in many respects from 
each other, but also most of those individuals and classes 
may be referred, each to an indefinite number of classes 
(as was formerly explained), according as we choose to 
abstract this point or that from each. 

Now to remind one, on each occasion, that so and so is 
referable to such and such a Class, and that the Class 
which happens to be before us comprehends such and 
such things, — this is precisely all thai is ever accomplished 
by Reasoning. 

For you may plainly perceive, on looking at any of the 
examples above, that when you assert both the Premises 
taken in conjunction, you have, virtually, implied the 
Conclusion. Else, indeed, it would not be impossible (as 
it is), for any one to deny the Conclusion, who admits 
both Premises. 

§ 8. Hence, some have considered it as a disparagement 
to a Syllogism (which they imagine to be one hind of 
Argument) that you can gain no new truth from it ; the 
Conclusions it establishes being, in fact, known already 
by every one who has admitted the Premises. 

Since, however, a Syllogism is not a certain distinct 
kind of argument, but any argument whatever, stated 
in a regular form, the complaint, such as it is, lies 
against Reasoning altogether. 

And it is undeniable, that no new truth, — in one sense 
of the word — (and that, perhaps, the strictest sense) can 
ever be established by Reasoning alone; which merely un- 
folds as it were, and developes, what was, in a manner, 
wrapped up and implied in our previous knowledge \ but 
which we are often as much unaware of, to all practical 
purposes, till brought before us, as if it had been wholly 
beyond our reach. 



Lesson xi.] information and instruction. 79 

New Truths, — in the strictest sense of the word — that 
is, such as are not implied in anything that was in our 
minds before, — can be gained only by the use of our 
senses, or from the reports of credible narrators, (fee. 

An able man may, by patient .Reasoning, attain any 
amount of mathematical truths; because these are all im- 
plied in the Definitions. But no degree of labour and 
ability would give him the knowledge, by "Reasoning" 
alone, of what has taken place in some foreign country; 
nor would enable him to know, if he had never seen or 
heard of the experiments, what would become of a 
spoonful of salt or a spoonful of chalk if put into water, 
or what would be the appearance of a ray of light when 
passed through a prism. 

§ 9. These two modes of arriving at any truth are per- 
ceived by all men as distinct. And they are recognised 
in the expressions in common use. The one is usually 
called "information'" the other "instruction."* We speak 
of trusting to the information (not the instruction) of our 
senses. Any one who brings news from any place, or who 
describes some experiments he has witnessed, or some 
spot he has visited, is said to afford us information. 

A Mathematician again, a Grammarian — a Moralist — 
any one who enters into a useful discussion concerning 
human life, — any in short who satisfactorily proves any- 
thing to us by reasoning, — is "said to afford us instruction. 

And in conversing with any one who speaks judiciously, 
one sometimes says " Very true I" or " That is a very just 
remark: that never struck me before," <fec. In these and 
such like expressions, we imply both that what he says is 
not superfluous, but valuable and important, and also that 
we are conscious of having ourselves possessed, in our own 
previous knowledge, the germ of what he has developed, 
and the means of ascertaining the truth of what he has 
said ; so as to have a right to bear our testimony to it. 

But when any one gives us information about a foreign 
Country, &c, though we may fully believe him, and be 
interested by what he tells us, we never think of saying 
"Very true!" or " You are quite right." We readily per- 

* It is not meant that this is the only sense of these words. 



80 compendium. [Part II. 

ceive that in this case the knowledge imparted is new to 
us in quite another sense ; and is what no reasoning alone 
could have imparted; being not implied in anything we 
knew already. 

These two modes of attaining what are, in different 
senses, new truths (and which, of course, are often mixed 
together,) may be illustrated by two different modes in 
which a man may obtain an addition to his wealth. One 
man, suppose, has property to a certain value, bequeathed 
to him; another discovers on his estate a mine of equal 
value. Each of these is enriched to the same degree. 
But the former of them acquires what he had, before, no 
right to; the latter merely comes to the knowledge and 
use of that which was before, legally, his property; 
though, till discovered, it brought him no advantage* 

Any mode of attaining knowledge, distinct from Rea- 
soning, is, of course, foreign from the present inquiry. 



LESSON XII. 



§ 1. The Dictum [or Maxim] above explained as the 
Universal-principle of Reasoning, will apply to a Syllo- 
gism in such a form as that of the examples given. 
"Every (or No) X is Y*; Z (whether some Z or every 
Z) is X; therefore — some, or every — Z is Y;" or "No Z 
is Yf or " Some Z is not Y;" as the case may be. 

And in that form every valid argument may be exhibited. 

But there are other Syllogisms in other forms, to which 
the "Dictum" cannot be immediately applied (though 
they may be reduced into the above form), and which yet 
are real Syllogisms, inasmuch as their conclusiveness is 
manifest from the form of expression, independently of 
the meaning of the Terms. 

For instance, "No Savages have the use of metals; the 
ancient Germans had the use of metals; therefore they 
were not savages," is a valid Syllogism, though the 
Dictum cannot be applied to it as here stated. But it 
may readily be reduced into the form to which the Dictum 

* See Lesson IX., § 7. 






Lesson xii.] terms of the conclusion 81 

does apply; by illatively converting the Major-premise, 
into "men who have the use of metals are not Savages." 

But the argument as it originally stood was a regular 
Syllogism; and so are some others also in a different form; 
although the Dictum does not immediately apply to them. 

Accordingly, certain rules [or "Canons"] have been 
framed which do apply directly to all categorical Syllo- 
gisms, whether they are or are not in that form to which 
the Dictum is immediately applicable. 

1st Canon. Two terms which agree with one and the 
same third, may be pronounced to agree with each other: 
and — 

2nd Canon. Two terms whereof one agrees and the 
other disagrees with one and the same third, may be 
pronounced to disagree with each other. 

The technical sense of the words "agree" and "disagree" 
has been explained in a former Lesson. 

The two terms which are each compared with the same 
third, are the Terms [or "Extremes"] of the Conclusion; 
viz.: the Major-term and Minor-term: and that third 
Term with which they are separately compared in the 
two Premises, is the Middle-term. 

On the former of these two Canons rests the proof of 
affirmative-conclusions; on the latter, of negative. 

§ 2. To take first a Syllogism in the form originally 
given: "Every X is Y; Z is X; therefore Z is Y;" or 
again, "No X is Y; Z is X; therefore Z is not Y;" in 
these examples, " Y" and "Z" are, in the two Premises 
respectively, compared with "X:" in the former example 
they are assumed to "agree" with it; and thence in the 
Conclusion, they are pronounced (according to the 1st 
Canon) to "agree" with each other; in the latter example, 
"Y" is assumed to "disagree" with "X," and "Z" to 
"agree" with it; whence in the Conclusion they are pro- 
nounced (according to the 2nd Canon) to "disagree" with 
each other. 

Again, to take a Syllogism in the other form, such as 
that in this Lesson, "No Savages," &c, or, "No Y is X; 
Z is X; therefore Z is not Y;" you will perceive that 
the 2nd Canon will apply equally well to this as to the 
preceding example. 



^2 compendium. [Part II. 

You Trill also find, on examination of the apparent- 
syllogisms [fallacies] — of which examples were given in 
former Lessons, and whose fatdtiness was there explained, 
— that they transgress against the above "Canons." 

Take for instance, "Some X is Y; Z is X; therefore Z 
is Y:"* and again " Every Y is X; Z is X; therefore Z 
is Y;" or "Every tree is a vegetable; grass is a vegetable; 
therefore grass is a tree;" in these (as was formerly ex- 
plained) the Middle-term is undistributed; [taken parti- 
cularly in both Premises;] the two "Extremes," therefore, 
[Terms of the Conclusion] have been compared each with 
part only of the Middle; and thence we cannot say that 
they have each been compared with one and the same 
third; so that we are not authorized to pronounce their 
agreement or disagreement with each other. 

But remember, that it is sufficient if the Middle-term 
be distributed in one of the Premises ; since if one of the 
" Extremes" (of the Conclusion) has been compared with 
part of the " Middle," and the other with the ivhole of it, 
they have both been compared with the same; since the 
whole must include every part. And accordingly, in the 
form originally given " Every X is Y: Z is X," &c, you 
may observe that the Middle-term is distributed in the 
Major-premise, and undistributed in the Minor. 

§ 3. Again, take the example formerly given, of "illicit 
process;" [proceeding from a term undistributed in the 
Premise, to the same, distributed, in the Conclusion;] as, 
"Every X is Y; Z is not X; therefore Z is not Y:" or, 
" Every tree is a vegetable; grass is not a tree; therefore 
grass is not a vegetable;" here the "Extremes" which 
in the Conclusion are compared together, are not really 
what had been compared, each with the Middle. For in 
the Conclusion, it is the ivhole of the term "vegetable" 
that is compared with the term "grass;" (since negatives 
distribute the Predicate,) though it was only part of 
that term had been, in the Premise, compared with 
"tree;" the Predicate of an "Affirmative" being undis- 
tributed. 

In this instance, therefore, as in the former one, the 

* See the example from Hume, respecting Testimony. 



Lesson xii.] ambiguous middle-term. S3 

Canons had not been complied with; each of these appa- 
rent-syllogisms having in reality four terms. 

You will observe also, that when the Middle-term is 
ambiguous, there are, in sense two Middle-terms, though 
you may have, apparently, a correct Syllogism: as "Light 
is opposite to darkness; feathers are light; therefore 
feathers are opposite to darkness." The word "Light" 
is here used equivocally. (See the explanation in Lesson 
"VII. § 3 of "univocal" and " equivocal.") 

So glaring an equivocation as this, could, of course, de- 
ceive no one, and could only be applied in jest.* But when 
there is a very small difference between the two senses in 
which a Middle-term is used in the two Premises, then, 
though the reasoning is not the less destroyed, the equivo- 
cation is the more likely to escape notice. And men are 
practically deceived in this manner, every day, both by 
others and by themselves. 

§ 4. For instance, there is an argument of Hume's (in 
the work referred to in a former example, and which is 
said to have been convincing to some persons) which may 
be regularly stated, thus: "Nothing that is contrary to 
experience can be established by testimony; every miracle 
is contrary to experience; therefore no miracle can be 
established by testimony." Now the middle-term, "con- 
trary to experience," admits of being understood in either 
of two senses : sometimes (and this is the strict and proper 
sense) it means "'what we know by our own experience 
to be false;" as, for instance, if several witnesses should 
despose to some act having been done at a certain time 
and place by a person known to me and in whose company 
I was at the time, and in a different place, I should 
be enabled to contradict their testimony from my own 
experience. 

Sometimes again the expression is employed to denote 
"something which we have never experienced, and have 
not known to be experienced by others;" which would 
be the case with the ascent of a Balloon, for instance, to 
one who had never seen or heard of such a thing; or with 



* Most jests, it is to be observed, — such as puns, conundrums, &c. — are 
mock fallacies. 



84 compendium. [Part II. 

the freezing of water, to a king of Bantam, mentioned 
by Hume. 

Now, if the Term " contrary to experience" be under- 
stood in this latter sense in both Premises, then the Major- 
premise of the Syllogism will be manifestly false; since 
it would imply that the king of Bantam, or any one living 
in a hot country, could have no sufficient reason for be- 
lieving in the existence of ice. And if the term be under- 
stood (in both Premises) in the other sense, then the Minor 
will be false; since a man cannot say that he knows by his 
own experience (whatever he may believe or judge, and how- 
ever rightly) the falsity of every individual narrative of 
every alleged miracle. 

But if the term is in each Premise to be so understood 
as that each shall be true, then it is evident that it must 
be taken as two different terms (in sense though not 
in sound) no less than the term " light" in the former 
example. 

§ 5. As for the truth or falsity of any Premise, or the 
sense in which any term is to be understood, in this or 
that Proposition, of course no fixed rules can be given; 
as this must evidently be determined in each case, by the 
subject-matter we are engaged on. 

But though no rules can be given for detecting and ex- 
'plaining every fallacious ambiguity, it is useful to learn 
and to keep in mind ivhere to seek for it; namely, to look 
to the Middle-Term, (the argument having been first stated 
in a syllogistic form) and to observe whether that is em- 
ployed precisely in the same sense in each Premise. 

As for the Terms of the Conclusion, there is not much 
danger of error or fallacy from any possible ambiguity in 
one of these; since in whatever sense either of these is 
employed in the Premise, it will naturally be understood 
in the Conclusion, in that same sense; though in itself, it 
might admit of other meanings. 

If, for instance, any one should conclude that the "Plan- 
tain" is "worth cultivation in places where it will flourish, 
because it produces a vast amount of human food," you 
would understand him to mean both in the Premise and 
the Conclusion, the fruit-bearing " Plantain" of the West- 
Indies, and not the herb that grows in our fields. 



Lesson xii.j terms of syllogism. 85 

Sometimes, however, in a long train of Reasoning, a 
person may be led into error, by remembering merely 
that a certain proposition has been proved, while he for- 
gets in what sense it was proved. 

§ 6. There are six rules commonly laid down, as result- 
ing from the two Canons above-mentioned; by which rules 
any apparent Syllogism is to be tested; since none can be 
objected to which does not violate any of these rules; and 
any apparent-syllogism which does violate any of them, is 
not, in reality, conformable to the above Canons. 

i. A Syllogism must have three, and only three Terms. 

ii. It must have three, and but three Propositions. 

iii. The Middle-term must be one only \i. e. not doable'], 
and therefore must be unequivocal, and must be, (in one 
at least of the Premises,) distributed. 

iv. No term is to be distributed in the Conclusion that 
was not distributed in the Premise : [or, there must be no 
"illicit-process."] 

v. One at least of the Premises must be affirmative; 
since, if both were negative, the Middle-term would not 
have been pronounced either to agree with each of the 
" Extremes," or to agree with one and disagree with the 
other; but to disagree with both; whence nothing can be 
inferred : as, " ]STo X is Y ; and Z is not X," evidently 
affords no ground for comparing Y and Z together. 

And vi. If one premise be negative, the Conclusion 
must be negative : since — inasmuch as the other Premise 
must be affirmative — the middle will have been assumed 
to agree with one of the " Extremes," and to disagree 
with the other. 

All these rules will have been sufficiently explained in 
what has already been said. 

And from these you will perceive, that in every Syllo- 
gism one Premise at least must be universal; since if both 
were Particular, there would be either an undistributed 
Middle, or an Illicit-process. 

For if each Premise were I (Particular-affirmative) there 
would be no distribution of any Term at all ; and if the 
Premises were I and O, there would be but one Term, — 
.the Predicate of O [the Particular-negative] — distributed ; 
and supposing that one to be the Middle, then the Con- 



86 compendium. [Part II. 

elusion (being of course negative, by rule vi.) would have 
its Predicate — the Major-term — distributed, which had 
not been distributed in the Premise. Thus, " Some X is 
Y ; some Z is not X," or again "some X is not Y ; some 
Z is X," would prove nothing. 

And for the like reasons, if one of the Premises be Par- 
ticular, you can only infer a Particular Conclusion : as 
"every X is Y; some Z is X," will only authorize you to 
conclude, " Some Z is Y," since to infer a Universal 
would be an " illicit-process of the Minor Term" 

§ 7. What is called the "Mood" [or "Mode"] of a 
Syllogism, is the designation of the three Propositions it 
contains (in the order in which they stand) according to 
their respective Quantity and Quality; that is, according 
as each Proposition is A, E, I, or O. 

Looking merely to the arithmetical calculation of per- 
mutations (as it is called), all the possible combinations of 
the four Symbols, by threes, would amount to 64. For 
each of the 4 admits of being combined, in pairs, with each 
of the 4 : [as A with A, with E, with I, and with O ; &c] 
which gives 16 pairs; and each of these 16 pairs admits 
of being combined with each of the 4 as a third; which 
gives 16x4—64. 

But it is plain that several of these combinations are 
such as could not take place in a Syllogism. For instance, 
E, O, O, could not be a Mood of any Syllogism, since it 
would have negative-premises (see rule v.), nor I, O, O, 
which would have both premises particular, nor I, E, O, 
which would have an illicit process of the Major-term; 
since the Conclusion being negative would have the 
Major-term distributed, while the Major-premise, being I, 
would have no term distributed, and so with many others. 

There will be found, on examination, to be in all only 
eleven Moods, in which any Syllogism can be expressed: 
and these are, A, A, A, — E, A, E, — A, I, I, — E, I, O, — 
A, E, E,— A, O, O,— A, A, I,— I, A, I— E, A, 0,-0, 
A, O— A, E, O. 

§ 8. What is called the "Figure" of a Syllogism, is the 
situation of the Middle-term, in the two Premises respec- 
tively, with relation to the two " Extremes'" [or Terms] 
of the Conclusion, — the Major and Minor Terms. 



Lesson xii] mood of a syllogism. 87 

It is evident that all the possible collocations of the 
Middle must be four ; since it must be either the Subject 
of the Major-premise and the predicate of the Minor ; or 
the Predicate of each; or the Subject of each; or the 
Predicate of the Major and Subject of the Minor. 

On looking to the examples originally given, you will 
see that a Syllogism in that form ["Every X is Y; Z is X; 
therefore Z is Y' 5 ] has the Middle-term made the Subject 
of the Major-premise, and the Predicate of the Minor. 

This is called the First Figure ; and it is to Syllogisms 
in this figure alone that the "Dictum" above-mentioned 
will at once apply. 

§ 9. If you look to the form afterwards exemplified: 
(§ 1 of this Lesson) as "No savages, &c." or "No Y is X ; 
Z is X ; therefore Z is not Y," you will see that the 
Middle is the Predicate of each Premise. This is called 
the Second Figure. And in this, evidently none but nega- 
tive Conclusions can be proved ; since one of the Premises 
must be negative, in order that the Middle-term may be 
(by being the Predicate of a Negative?) distributed. 

Again, the Middle-term may be the Subject of each Pre- 
mise. And this is called the Third Figure. Thus "Some 
X is Y ; every X is Z ; therefore some Z is Y ;" is a cor- 
rect Syllogism in the Third Figure, being conformable to 
the first Canon. 

And the Syllogism here given as an example may be 
easily reduced to the First Figure, by simply converting the 
Major-premise, and taking it for the Minor ; [transposing 
the Premises ; ] which will enable you to infer the simple- 
converse of the Conclusion : as " Every X is Z ; some 
Y is X ; therefore some Y is Z :" and this implies that 
" some Z is Y ;" since (as was explained formerly) the 
simple conversion of I is illative. 

For instance, " some painful things are salutary ; every 
thing painful is an object of dread : therefore some things 
which are objects of dread are salutary ;" this, though a 
valid Syllogism as it stands, may be reduced, in the man- 
ner above stated, to the First Figure. 

In this, or in other ways, any Syllogism in the Third 
Figure may be easily "reduced" (as the technical phrase 
is) to the First Figure, 



88 compendium. [Part II. 

In this Third Figure you will find that none but Par- 
ticular Conclusions can be drawn. To infer a Universal 
would always, you will find, involve an " illicit jrrocess of 
the Minor-term." For if the Premises are both Universal, 
(which as we have already seen (§6) they must always 
be, to warrant a Universal Conclusion,) then, supposing 
them to be A, A, there will have been, — in this Third 
Figure — no term distributed except the Middle; (affirma- 
tives not distributing the Predicate;) and consequently 
no term can be distributed in the Conclusion ; which must 
therefore be I. 

And if the Premises be E and A, there will have been 
(besides the middle) only one term, — the Predicate of E, 
distributed ; and consequently only one term can be dis- 
tributed in the Conclusion; and that one must be the 
Predicate of O ; since the Universal [E] would have both 
terms distributed. 

§ 10. The Third Figure might be called the " exceptive" 
or the "refutatory" Figure; (or, agreeably to the expres- 
sion of the Greek writers, the " enstatic ;") as being a very 
natural form of expressing arguments which go to establish 
the contradictor]/ of some Universal Proposition that any 
one may have maintained, or that may be generally 
believed. 

For instance, if any one were speaking of " metals " as 
being, universally, "conductors of heat," you might adduce 
" Platina" as an exception. Or should any one contend 
that "no agent incapable of distinguishing moral good and 
evil (as for instance a madman) can be deterred from any 
act by apprehension of punishment," you might refute 
this, by adducing the case of a brute, — for instance, a 
dog — deterred from sheep-biting by fear of punishment. 
And such arguments would fall very naturally into the 
Third Figure. 

It is, especially, the most natural form in which to ex- 
press an argument — such as we often employ for the above 
purpose — in which the Middle-term is a Singular-term ; 
as when, for instance, you prove, by the example of a cer- 
tain individual,* the contradictory of a proposition (which 
would seem to most persons a very probable conjecture) 

* See the Note on a former Lesson, on the case of Laura Bridgeman. 



Lesson xiii.] figure of syllogism, 89 

that a deaf and dumb person, born blind, cannot be taught 
language. 

The Second Figure may be called the "exclusive" Figure; 
being a very natural form for arguments used in any 
inquiry in which we go on excluding, one by one, certain 
suppositions, or certain classes of things, from that whose 
description we are seeking to ascertain. 

Thus, certain symptoms, suppose, exclude, "Small 
Pox" that is, prove this not to be the patient's disorders- 
other symptoms, suppose, exclude "Scarlatina" &c, and 
so one may proceed, by gradually narrowing the range of 
possible suppositions. 

These three Figures are the only ones in which any 
argument would, designedly, be stated. For, as to tahat 
is called the Fourth Figure (in which the Middle-term is 
made the Predicate of the Major-premise and the Subject 
of the Minor) though a Syllogism so stated would be un- 
deniably valid if conformable to the rules (as "every Y 
is X; no X is Z; therefore no Z is Y"), this form is only a 
clumsy and inverted way of stating what would naturally 
be expressed in the First Figure; as, in this example, 
might be done by transposing the Premises, and simply 
converting the Conclusion. 



LESSON XIII. 



§ 1. Besides Categorical-arguments, which we have been 
treating of, Reasoning is often expressed in a Hypothe- 
tical form. And though such arguments may be reduced 
into categorical form, this is not necessary, except for the 
purpose of pointing out the sameness in all cases of the 
Reasoning-process. For you may exhibit in a hypotheti- 
cal form a perfect "Syllogism" as above denned. 

A Hypothetical (or as some writers call it, a " com- 
pound") Proposition, consists of "two or more Categorical 
propositions, united by a Conjunction, in such a manner 
as to make them one proposition." And the different 
kinds of hypothetical-proposition are named after their 
respective Conjunctions; namely, "Conditional" and 



90 compendium. [Part II. 

"Disjunctive."* For instance, "if A is B, then X is Y," 
is a Conditional-Proposition ; t "either A is B, or X is Y" 

is Disjunctive. 

And each of these is a real Projjosition, i.e. asserts some- 
thing; and consequently is either true or false; which (as 
was formerly explained) is peculiar to Propositions ; and 
each is also one Proposition, though consisting of several 
parts [or "members"] each of which if taken separately 
would be itself a proposition; but the Conjunction (which 
is called the Copula) makes the whole one Proposition. 

§ 2. For instance, "the world is eternal," is a proposi- 
tion; "records earlier than the Mosaic exist," is another 
proposition; and "if the world be eternal, records earlier 
than the Mosaic must exist," is a third proposition distinct 
from each of the others, and which may be true, though 
they be both false ; since it does not assert the truth of 
either of them, but only the connexion between them. 
Again, should any one say "if the Northern-lights be 
shining, some great revolution of an empire is going on," 
this would be, properly speaking, a false Proposition, even 
should it turn out that each of the "members" stated as 
a categorical proposition is true; supposing it admitted 
that they have no connexion with each other. 

Observe, however, that no false conclusion can be de- 
duced from a false Conditional-proposition, when it so 
happens that both its "members" (stated as categorical- 
propositions) are true. 

In the case of a Disjunctive-proposition, on the other 
hand, it is implied, that one at least of its "members" 
(stated as a categorical-proposition) must be true, and 
that if not, the whole proposition must be false. As, "this 
man was either at Oxford or at Cambridge" would not be 
true, if he were not at Oxford, and not at Cambridge. 

And it is usually meant to be understood that only one 
of the members can be true; for if this were not the 
meaning in such an example as the foregoing, it would 
have been more correct to say "this man was either at 
Oxford, or Cambridge, or both." 

* See Lesson X. 
t Those writers who use the word compound-proposition instead of hypothe- 
tical, employ "hypothetical" to signify "conditional." 



Lesson xiii.] hypothetical-propositions. 91 

§ 3. A Hypothetical-syllogism, is one in which the rea- 
soning itself turns on the Hypothesis; not, every syllogism 
that has in it a hypothetical premise; for the " hypothesis" 
may be a portion of one of the Terms, and the syllogism 
may be merely categorical. 

For instance, " Real miracles are evidence of a divine 
commission ; if the works of Jesns were acknowledged 
miraculous by the unbelieving Jews, they must have 
been real miracles ; therefore the works of Jesus (if they 
were acknowledged, &c.,) are evidence of a divine com- 
mission;" is a categorical syllogism; the hypothesis being 
merely a portion of the Minor-term. 

And so also with such an example as " Every X is either 
Y or W ; Z is X ; therefore Z is either Y or W." 

In a hypothetical-syllogism, properly so called, — that 
is, in which the reasoning is based on a hypothetical pre- 
mise, that premise is called the Major, and the other — 
which is categorical — is called the Minor-premise. 

"We will first speak of Conditional-syllogisms. 

There are, in a Conditional-proposition, two members 
[categorical propositions] whereof one is asserted to 
depend on the other. That on which the other depends 
is called the "Antecedent ;" that which depends on it, 
the "Consequent;" and the connexion between the two, 
I (expressed by "if" or "supposing,") is called the "con- 
sequence." 

(Consequence) (Antecedent) 

For instance " If this man is a murderer 

(Consequent) (Consequent) 

1 he deserves death." "The English are well off 

( (Consequence) (Antecedent) 

if they know their own advantages." 

The natural order is to place the "'Antecedent" first ; 

I but this (as you will see from the example above) is not 
essential. 

§ 4. The meaning, then, of a Conditional proposition, 

i is, that "the Antecedent being assumed to be true, the Con- 
sequent is to be granted as true also." And this may be 
considered in two points of view : 1st, allowing that the 
Antecedent is true, the Consequent must be true ; 2ndly, 
supposing the Antecedent were true, the Consequent would 
be true. 



92 compendium. [Part II. 

Hence, there are two kinds of Conditional-syllogism ; 
1st, if the Antecedent be (in the minor-premise) granted 
to be true, the Consequent may ( in the Conclusion ) be 
inferred : 2nclly, if the Consequent be not true — that is, 
if its Contradictory be assumed in the minor-premise — the 
Antecedent cannot be true \ that is, its Contradictory may, 
in the Conclusion, be inferred : since if the Antecedent 
had been true, the Consequent (which we have assumed to 
be false) would have been true also. 

A Syllogism of the former kind, is called "Cooisiructive" 
of the latter kind " Destructive.''' 

For instance, if " A is B, X is Y:" let this be the major- 
premise; then, if you add, "but A is B ; therefore X is Y," 
this forms a Constructive-syllogism ; if you say " X is not 
Y; therefore A is not B;" this is a Destructive-syllogism. 
Thus "if this river has tides, the sea into which it flows 
must have tides;" then if I add "this river has tides," it 
follows in Conclusion, that "the sea into which it flows 
has tides ;" which is a Constructive-syllogism. If I add 
"the sea into which it flows has no tides," it follows that 
" this river has no tides." 

§ 5. And here observe, by the way, that in hypotheti- 
cal-arguments we are not concerned with the distinction 
between affirmative and negative C inclusions. For, of the 
two members of a Conditional- Proposition, either, or both, 
may be affirmative, or may be negative ; so that we may 
establish the truth " constructively" of either an affirma- 
tive or a negative Consequent ; or may ("destructively") 
establish the falsity — that is, infer the Contradictory — of 
either an affirmative or negative Antecedent. 

For instance, "if no miracles had been displayed by 
the first preachers of the Gospel, they could not have 
obtained a hearing ; but they did obtain a hearing ; 
therefore some miracles must have been displayed by 
them ;" is a Destructive-conditional-Syllogism. 

The Consequent, as has been said, depends on the 
Antecedent ; so that, if the Antecedent be true, the Conse- 
quent will be true also ; but as the Antecedent does not 
depend on the Consequent, nothing is proved by denying 
the Antecedent, or again, by assuming the truth of the 
Consequent. Suppose it granted, that " if A ia B, X is Y," 



Lesson xiii.] conditional-proposition. 93 

though it may indeed so happen that X is Y, only on iliat 
condition, — that is, that if X is Y, A is B, — this is not 
implied by the original assertion; so that (merely assum- 
ing that original assertion), to add that "A is not B," or 
again, to say " X is Y," proves nothing. 

For instance, "if this man has committed theft, he de- 
serves punishment," does not authorize me to proceed 
either to say "he has not committed theft; therefore he 
does not deserve punishment;" or again, "he deserves 
punishment; therefore he has committed theft." For it 
is (in this case) evident that a man may deserve punish- 
ment for some other offence. 

§ 6. And you may observe, that the fallacy of affirming 
the Consequent and thence inferring the truth of the Ante- 
cedent, answers to the fallacy (in Categoricals) of undis- 
tributed-middle or to that of negative-premises ; as may 
be seen from the above example. For to say, "'every one 
who has committed theft deserves punishment; and this 
man deserves punishment," would evidently be a case of 
undistributed Middle. And again, if instead of saying "if 
this man has a fever, he is not fit to travel; and he is 
not fit to travel; therefore he has a fever," you say "no 
one who has a fever is fit to travel," <fec., there will be 
the fallacy of two negative-premises. 

The fallacy again of denying the Antecedent, and thence 
inferring the denial of the Consequent, would correspond 
(in Categoricals) either to an "illicit-process of the Major- 
term," or to the Fallacy of "two negative-premises," or 
that of introducing palpably "more than three terms." 
For instance, suppose instead of saying " If this man has 
committed theft," (fee. you say, " Every one who has com- 
mitted theft deserves punishment; this man has not 
committed theft," ifec. this would be an illicit-process of the 
Major. Or again, suppose, instead of saying, "If this man 
has a fever, he is not fit to travel ; but he has not a fever ; 
therefore he is fit to travel," you say, "No one who has a 
fever is fit to travel ; this man has not a fever," (fee, this 
would be to employ "two negative-premises." Again, "If 
this army is not brave it will not be victorous ; it is brave ; 
therefore it will be victorious;" would, if expressed cate- 
gorically, have palpably more than three terms. 



94 compendium. [Part II. 

§ 7. It is plain, from what has been above said, that a 
Conditional-proposition may be illatively converted, by tak- 
ing the Contradictory of the Consequent for an Antecedent 
and (of course) the Contradictory of the Antecedent for a • 
Consequent. "If A is B, X is Y," implies that "if X is not 
Y, A is not B." " If all wages be regulated by the price 
of food, an English labourer will have higher wages than 
an American;" this manifestly implies, that, "if an Eng- 
lish labourer has not higher wages than an American, all 
wages are not regulated by the price of food. 

This corresponds to the conversion of the categorical- 
proposition A, "by negation;" ["contraposition;"] every 
Conditional-proposition corresponding in fact to a Uni- 
versal-anirmative-Categorical; the Antecedent answering 
to the Subject; and the Consequent, to the Predicate. 

It is evident, that if you thus convert the Major-premise 
[the hypothetical-premise] of any Conditional-syllogism, 
you change the Syllogism from "Constructive" to "Des- 
tructive" or vice versa from Destructive to Constructive. 

The Proposition "if A is B, X is Y" maybe considered 
as amounting to this ; "The case [or supposition] of A being 
B, is a case of X being Y." And then to say (as in the 
Minor-premise and the Conclusion, of a constructive-con- 
ditional syllogism) "A is B; and therefore X is Y," is 
equivalent to saying "the present [or the existing] case is 
a case of A being B ; therefore this is a case of X being Y." 

Or again, "if the Stoics are right, pain is no evil; but 
pain is an evil; therefore the Stoics are not right," (which 
is a destructive-conditional syllogism,) may be reduced to 

a Categorical, thus: "To say that pain is no evil is 

not true; to say that the Stoics are right is 

to say that pain is no evil; therefore to say that 

the Stoics are right is not true." 

This Syllogism is in the First Figure. The argument 
might be exhibited in the Third Figure, thus: "that pain 
is no evil is not true ; but that is maintained by the Stoics ; 
therefore something maintained by the Stoics is not true." 

In some such way (taking care always to preserve the 
same sense) any argument may be exhibited in various dif- 
ferent forms of expression, (the choice of which is merely 
a matter of convenience,) so as to point out and impress on 



Lesson xiii.] conditional-proposition. 95 

the mind that the reasoning-process itself is always essen- 
tially one and the same, and may ultimately be referred 
to the " Dictum" formerly mentioned. 

§ 8. In a disjunctive proposition, as has been already 
observed, it is implied, that at least some one of the "mem- 
bers" must be true. If therefore all except one be (in the 
Minor-premise) denied, the truth of the remaining one 
may be inferred. 

For instance, " either the Gospel was an invention of 
impostors, or it was a dream of fanatics, or a real reve- 
lation; it was neither of the two former; therefore it 
was a real revelation." 

But if there be more than two members, and you deny 
(in the Minor-premise) one or more of them, but not all 
except one, then you can only draw a disjunctive Conclusion : 
as, " this event occurred either in Spring, Summer, Autumn, 
or Winter; it did not occur in Summer or in Winter ; 
therefore it occurred either in Spring or in Autumn." 

In a disjunctive-proposition it is (as has been said above) 
usually understood that the members are exclusive ; i. e. 
that "only one of them can be true ; and you may, on that 
supposition, infer from the truth of one of them (assumed 
in the Minor) the Contradictory of the other, or others. 
As " either A is B, or C is D, or X is Y: but A is B; 
therefore C is not D, nor is X Y." 

§ 9. A Disjunctive-syllogism may readily be reduced to 
a Conditional, by merely altering the form of the Major 
premise; namely, by taking as an Antecedent the Contra- 
dictory of one or more of the members; everything else 
remaining as before. Thus, in the example lately given, 
you might say " If this did not occur in Summer, nor 
in Winter, it must have occurred either in Spring or in 
Autumn;" &c. 

A Disjunctive-proposition, you are to observe, is, (as 
well as a Conditional, ) always affirmative. For, either kind 
of Hypothetical proposition always affirms the connexion 
of the members of it, [categorical-propositions contained in 
it,] whether these be affirmative or negative propositions. 

And the contradiction of a Hypothetical-proposition must 
therefore consist in denying this connexion; which is done, 
not in a Hypothetical, but in a Categorical proposition* 



96 compendium. [Part II. 

When it is asserted, that "if A is B, X is Y" you would 
contradict this by saying " it does not follow that if A is B, 
X must be Y ;" or by some such expression. Or when it 
is asserted that " either A is B, or X is Y, " you might 
contradict this, by saying u it is possible that neither A is B, 
nor X Y f or you might contradict a Disjunctive-propo- 
sition by two or more Categorical propositions ; namely, 
by asserting separately the Contradictory of each member; 
as " either some Z is Y, or else some W is not X," might 
be contradicted by "no Z is Y, and every W is X." 



LESSON XIV. 



§ 1 . It will often happen, that you will have occasion to 
employ that complex kind of Conditional-syllogism (con- 
sisting of two or more such syllogisms combined) which is 
commonly called a "Dilemma." 

When you have before you as admitted truths two (or 
more) Conditional-propositions, with different Antece- 
dents, but each with the same Consequent, and these 
Antecedents are such that you cannot be sure of the truth 
of any one of them separately, but are sure that one or 
other must be true, you will then naturally be led to state 
both of the Conditional-propositions first ; and next, to 
assert disjunctively the Antecedents ; and thus to infer the 
common Consequent. As " if every A is B, X is Y; and if 
some A is not B, X is Y; but either every A is B, or some 
A is not B ; therefore X is Y." 

This kind of argument was urged by the opponents of 
Don Carlos, the pretender to the Spanish Throne ; which 
he claimed as heir-male, against his niece the queen, by 
virtue of the Salic law excluding females ; which was 
established (contrary to the ancient Spanish usage) by a 
former king of Spain, and was repealed by King Ferdi- 
nand. They say, " if a king of Spain has a right to alter 
the law of succession Carlos has no claim ; and if no king 
of Spain has that right, Carlos has no claim ; but a king 
of Spain either has or has not, such right; therefore (on 
either supposition) Carlos has no claim." 



Lesson xiv.] dilemma. 97 

§ 2. When several Conditional-propositions have dif- 
ferent Consequents as well as different Antecedents, then 
we can only disjunctively infer those Consequents : that 
Is, we can only infer that (supposing some one or other of 
the Antecedents true) one or other of the Consequents must 
be true. As " if A is B, X is Y; and if C is D, P is Q j 
but either A is B, or C is D; therefore either X is Y, or 
P is Q." Thus "if the obedience due from Subjects to 
Rulers extends to religious worship, the ancient Christians 
are to be censured for refusing to worship the heathen 
idols; if the obedience, etc., does not so extend, no man 
ought to suffer civil penalties on account of his religion ; 
but the obedience, &c., either does so extend, or it does 
not ; therefore either the ancient Christians are to be cen- 
sured, <fec., or else no man ought to suffer civil penalties 
on account of his religion." 

So also, ''if a man is capable of rising, unassisted, from 
a savage to a civilized state, some instances may be pro- 
duced of a race of savages having thus civilized them- 
selves; and if Man is not capable of this, then, the first 
rudiments of civilization must have originally come from 
a superhuman instructor; but either Man is thus capable, 
or not ; therefore either some such instance can be pro- 
duced, or the first rudiments," (fee. 

§ 3. And when there are several Antecedents each with 
a different Consequent, then, we may have a Destructive- 
dilemma : that is, we may, in the Minor-premise disjun- 
ctively deny the Consequents, and in the Conclusion dis- 
junctively deny the Antecedents. Or again, you may have 
a Dilemma partly Constructive and partly Destructive; 
that is, in the Minor-premise (which in a Dilemma Is 
always a disjunctive-proposition) the members — suppose 
for instance there are two, — may be, one of them, the 
assertion of the Antecedent of one of the Conditional- 
propositions, and the other, the contradictory of the Con- 
: sequent of the other Conditional. 

Suppose we say, "if X is not Y, A is not B; and if P 
is not Q, C is not D; but either A is B, or C is D; there- 
fore either X is Y, or P is Q;" this would be a Destruc- 
tive-Dilemma; and you may see that it corresponds ex- 
actly with the example given a little above, only that we 
E 



93 compendium. [Part II. 

have, here, converted both, of the Conditional-propositions. 
(See § 7 of the preceding Lesson). If we had converted 
one only, and not the other, of the Conditionals (as "if A 
is B, X is Y; and if P is not Q, C is not D ;" &c.), then 
the Dilemma would have been partly Constructive, and 
partly Destructive. For, as has been formerly explained, 
the Difference between a Constructive and Destructive 
Syllogism consists merely in the form of expression, and 
it is very easy to reduce either form into the other. 

It may be worth while to observe, that it is very com- 
mon to state the Minor-premise of a Dilemma first ; in 
order to show the more clearly that the several Categorical 
propositions which are, each, doubtful, when taken sepa- 
rately, may be combined into a Disjunctive-proposition 
that admits of no doubt. And this Minor-premise being 
disjunctive, some have hence been let! to suppose that a 
Dilemma is a kind of disjunctive argument ; though it is 
really, as we have shown, a Conditional. 

The name of "Z^'lemma," again, has led some to sup- 
pose that it must consist of two members only; though it 
is evident that there may be any number. 

§ 4. When there is a long Series of arguments, the 
Conclusion of each being made one of the Premises of the 
next, till you arrive at your ultimate Conclusion, it is of 
course a tedious process to exhibit the whole in the form 
of a series of Syllogisms. This process may, in many cases, 
be considerably abridged, without departing from the 
strict syllogistic form: [that is, such a form as shows the 
conclusiveness of the reasoning, from the expression 
alone, independently of the meaning of the Terms, and 
equally well when arbitrary Symbols are used to stand 
for the Terms]. 

"What is called a "Sorites" (from a Greek word signify- 
ing a heap, or pile) is such an abridged form of stating a 
train of arguments. When you state a series of proposi- 
tions in which the Predicate of the first is made the Sub- 
ject (distributed) of the next, and the Predicate of that, 
again, in like manner, the Subject of the next, and so on, 
to any length, you may then predicate in the Conclusion, 
the Predicate) of the last Premise of the Subject of the 
first. 



Lesson xiv.] sorites. 99 

Thus "A (either "some''' or "every") is B; every B is C; 
every C is D ; every D is E; &c., therefore A is E ;" or 
"no D is E; therefore A is not E." Thus also, "'this 
mm is selfish ; whoever is selfish is neglectful of the good 
of others ; whoever is neglectful of the good of others is 
destitute of friends ; and whoever is destitute of friends 
is wretched; therefore this man is wretched." 

§ 5. To such a form of argumentation the " Dictum" 
formerly treated of, may be applied, with one small addi- 
tion, which is self-evident. Whatever is affirmed or 
denied of a whole Class, may be affirmed or denied of 
whatever is comprehended in [any class that is wholly com- 
prehended iii] that Class." This sentence, omitting the 
portion enclosed in brackets, you will recognise as the 
"Dictum" originally laid down: and the words in brackets 
supply that extension of it which makes it applicable to a 
" Sorites," of whatever length; since it is manifest that 
that clause might be enlarged, as far as you will, into "a 
Class that is wholly comprehended in a class, which again 
is wholly comprehended in another Class," <fcc. 

You will perceive, on looking at the above examples, 
that, though the first of the propositions of a Sorites may 
be either Universal or Particular, all the succeeding 
Premises must be Universal; since, else, the "Dictum," 
as stated just above, would not apply. 

You will perceiA^e also that though the last of the Premises 
may be either Negative or Affirmative, all the preceding- 
ones must be Affirmative, in order that the Dictum may be 
applicable. Thus, in the example first given, it is allowable 
to say " no D is E : therefore A is not E ;" but then it is 
necessary that "C" should be comprehended in "D" (not ex- 
cluded from it) and "B" likewise in " C " and "A" in "B," 
since otherwise the " Dictum " would not be applicable. 

§ 6. It will be seen, on examining the examples, that 
there are in a Sorites as many Middle-terms as there are 
intermediate propositions between the first and the last ; 
and that it may be stated in just so many separate syllo- 
gisms in the First Figure ; which is the simplest and 
most common form of a Syllogism. 

The first of these Syllogisms will have for its Hajor- 
premise the second of the propositions in the series, and for 



100 compendium. [Part II. 

its Jimor-premise, the first of them ; and the Conclusion 
of this first syllogism will be a proposition which is (in 
the Sorites) not expressed but understood ; and which 
will be the Minor-premise of the next Syllogism. And 
of this next syllogism the Major-premise will be the third 
that is expressed in the Sorites ; and so on. 

For instance (1st), "every B is C ; A is B;" ["therefore 
A is C"] ; (2ndly), " every C is D ;" ["A is C ; therefore 
A is D"], &c. 

The portions enclosed in brackets are those which in 
the Sorites are understood. 

The only J/mor-premise expressed in the Sorites is the 
first proposition of the Series; all the succeeding Minor- 
premises being understood. 

And hence it is that (as has been above said) this first 
is the only one of all the Premises that may allowably be 
a Particular : because, in the first Figure, though the 
Minor may be either Universal or Particular, the Major 
(as you see from what was formerly said of the "Dictum"), 
must always be Universal ; and all the premises in the 
Sorites, except the first, are JS/a/or-premises. 

In this way may also be explained what was above said, 
that the last of the premises of a Sorites is the only one 
that can allowably be a Negative; since if any of the 
others were negative, the result would be that one of the 
Syllogisms of the Series would have a negative Minor- 
premise; which in the first Figure (as you will see by 
again referring to the " Dictum") is inadmissible. 

§ 7. A Series of Coiiditional-syllogisms (which corre- 
spond, as has been shown, to Categorical-syllogisms in the 
first Figure) may in like manner be abridged into a Sorites; 
by making the Consequent of the first proposition the 
Antecedent of the next ; and so on : and then drawing the 
Conclusion by either asserting the first Antecedent, and 
thence (constructively), inferring the last Consequent, or 
else, denying the last of the Consequents, and (destruc- 
tively) inferring the Contradictory of the first Antecedent. 
As "if A is B, C is D; and if C is D, E is F; and if E 
is F, G is H," &c. : and then if the Sorites be "Construc- 
tive," you add " but A is B, therefore G is H ;" or, if 
"destructive," but " G is not H : therefore A is not B." 



Lesson xiv.] enthymeme. 101 

The foregoing are all the forms in which Reasoning can 
be exhibited Syllogistically ; i. e. so that its validity shall 
be manifest from the mere form of expression. 

For, an Enthymeme (see Lesson II. § 3) is manifestly 
not syllogistic; since it is possible to admit the trnth of 
the one premise that is expressed, and yet to deny the 
Conclusion. 

An Enthymeme may indeed be such (since it contains 
all the three Terms requisite for a Syllogism,) that we can 
readily perceive what the premise is that ought to be under- 
stood, and which, i/* supplied, would make the Syllogism 
complete: as "Z is X; therefore Z is Y;" [or " the Elk 
has horns on the head ; therefore it is a ruminant :"] this 
would be syllogistic, if you. were to prefix "Every X is Y;" 
but whether this be the Premise actually meant to be un- 
derstood, we can only judge from the sense of the words 
that are expressed, and from what we believe respecting 
the subj ect-matter in hand, and the design of the speaker. 

In a Syllogistic form, on the other hand — whether Ca- 
tegorical or Hypothetical, and whether at full length, or 
abridged into a Sorites — that which is actually expressed 
in the Premises is such that no one can possibly suppose 
these true (whatever be the meaning of the Terms or 
whether we understand them or not) ivithout admitting the 
truth of the Conclusion thence drawn. 

§ 8. As for any arguments that are not expressed in a 
regular form, of course no precise rules can be laid down 
for reducing them into such a form; since any arguments 
to which such rules do apply must evidently be, on that 
very ground, pronounced to be already syllogistic. Some 
general remarks, however, (drawn chiefly from what has 
been taught in the foregoing Lessons,) maybe practically 
serviceable in the operation of reducing arguments into 
regular form. 

i. It has been remarked (in Lesson III. § 7), that men 
are very impatient of tedious prolixity in Reasoning; and 
that the utmost brevity, — the most compressed statement 
of argumentation, — that is compatible with clearness, — is 
always aimed at, and is indeed conducive to clearness. And 
hence (as was pointed out), a single sentence, — or even a 
word — will often be a sufficient hint of an entire syllogism. 



102 compendium. [Part II. 

And it may be added, that such a sentence will some- 
times be in the form, not of a Proposition, but of an Ex- 
clamation, — a Question, — or a Command ; and yet will be 
such as readily to suggest to the mind a Proposition. 

For instance, in some of the examples lately given, one 
might say (in the place of one of the Propositions) " Choose 
which you will of these two suppositions ;" or " who can 
doubt that so and so follows]" 

The message to Pilate from his wife* furnishes an in- 
stance of a single word ("just" J suggesting a Major-pre- 
mise, while the Conclusion is stated in the form of an 
exhortation: "Have thou nothing to do with that just 
man." And the succeeding sentence must have been 
designed to convey a hint of Arguments for the proof of 
each of the Premises on which that Conclusion rested. 

§ 9. ii. Remember that (as was formerly shown) we 
may change any proposition from Affirmative to Negative, 
or vice versa, without altering the sense: it beino- the 
same thing, for instance, to affirm of any one the term 
"not happy/'' or to deny "happy/' So that an argument 
may be valid which might appear at the first glance to 
have "negative-premises/ 7 

But if the above experiment be tried in an argument 
that is really faulty on that ground, the only effect will 
be, to change one fallacy into another: as "A covetous 
man is not happy; this man is not covetous; therefore 
he is happy;" here, if you take "happy" as the predicate 
of the Major, you have negative-premises: if you take 
"not happy" [or "unhappy"] as the term, you will have 
four terms. 

On the other hand, "no one is happy who is not content; 
no covetous man is content ; therefore no covetous man 
is happy," is a valid syllogism. 

That the Conversion-by-negation [contra-position] of 
a Universal-affirmative is illative, has been formerly ex- 
plained. And it is very common, and often conducive to 
clearness, to state such a proposition (A) in the form of 
this its converse (E) ; as, for instance, instead of " every 
motive that could have induced this man to act so and so, 

* Matt, xxvii. 19. 



Lesson xiv.l conversion-by-negatiox. 103 

must have been purely benevolent/ ' to say, "no motive 
but pure benevolence could have induced him to act so." 

iii. ^Remember that one single sentence (as was form- 
erly explained, Lesson IX. §7) may imply several distinct 
propositions, according to the portions of it which you 
understand as the Subject, and as the Predicate. For 
instance, "It is the duty of the Judge to decide for him 
who is in the right ; this plaintiff is in the right ; there- 
fore it is the Judge's duty to decide for him," might be 
understood as having five terms: but according to the 
drift of the first premise (considered as a part of this 
argument) what you are speaking of is, not " the duty 
of the Judge," but " the person who is in the right ;" of 
whom you assert that "he is fairly entitled to the Judge's 
decision on his side." And if thus stated, the argument 
will be seen to be valid. 

And here it may be remarked, that to state distinctly 
as Subject and Predicate, that which is really spoken of, 
and that which is said of it, will be often the best and 
most effectual exposure of a Fallacy; which will always be 
the more likely to escape detection, the more oblique and 
involved is the expression. 



104 

PA.RT III. 
SUPPLEMENT. 



LESSOX XV. 



§ 1. There are some other technical terms, which it is 
useful to be familiar with, and which we will therefore 
now proceed to treat of in a supplementary Lesson. They 
are such as are usually introduced in an earlier place, pre- 
viously to the matter of the last five Lessons. But it has 
been thought better to postpone everything that was not 
indispensable for the right understanding of what has 
been said concerning the several forms of Syllogism. 

A " Common-term," we have seen, is so called from its 
expressing what is common to several things: and is 
thence called also a " Predicable," inasmuch as it can be 
aMrmaiiYelj-predicated, in the same sense ["univocally"] 
of certain other terms. It is evident, that the word "Pre- 
dicable" is relative, i. e. denotes the relation in which some 
Term stands to some other, of which it can be predicated. 
And this relation is of different kinds; in other words 
there are several Classes [or Heads] of Predicables. 

"When you are asked concerning any individual thing, 
" What is it?" the answer you will give, if strictly correct, 
would be what is technically called its " Species:' 
"this is a, pen;" "that is a man;'' "this is a circle;' "that 
is a magnet" etc. 

And the "Species" of anything is usually described in 
technical language as expressing its "whole essence;" 
meaning the whole of what can be expressed by a Com- 
mon-term : for it is plain that (as was formerly shown) it is 
only by taking an inadequate view of an "Individual," so 
as to abstract from it what is common to it with certain 
other individuals, di ishesitfroin 

them (including its acta object) — it 

is only then, I say, that we can ob Common- 

:. When the same question "What is ; 

. the term by which you answer, is, that 
Predicable which is technically called the "Genus" of that 



Lesson xv.] difference. 105 

Species. As,, "What is a,pen£" answer, an "Instrument;" 
[a kind or species of Instrument ;] " What is a circle']" 
" A oiirvilinear-plane-figure :" so also "a Magnet" "would 
be said to be a " Species [or kind] of Iron ore," &c. 

When you are asked "What kind of [or "what sort of] 
instrument is a pen?" you would answer, One designed 
for writing/' this being what characterizes it, and distin- 
guishes it from other instruments; "What kind of animal 
is Man?' the answer will be "'Rational;" as distinguish- 
ing the Species from other animals; "What kind of plane- 
cur vilinear-ngure is a circle?" answer "'One whose circum- 
ference is everywhere equidistant from the Centre;" which 
circumstance distinguishes it from an Ellipse : &c. 

Such a Predicable then is technically called the "Dif- 
ference;" [or by the Latin name "Differentia;"] in pop- 
ular language, frequently, the "'Characteristic," or the 
"distinguishing point." And the " Difference" together 
with the "Genus," are technically spoken of as "consti- 
tuting ["'making-up"] the " Species." 

Any quality [or "attribute"] which invariably and 
peculiarly belongs to a certain Species, but which yet is 
not that which we hx on as characterizing the Species, 
is technically called a ''Property" [or " Proprium"] of 
th.it Species. Thus "risibility" [or the faculty of laugh- 
ter] is reckoned a " Property" of Man: one of the " Pro- 
perties" of a Circle is, that any angle drawn in a semi- 
circle is a right -angle : occ. 

The power of "attracting iron" might be taken as the "dif- 
ference [or "'characteristic'] of a Magnet: and its "Polarity" 
as a "'Property:" or again, this latter might be taken as 
its Difference, and the other reckoned among its Properties. 

For it is evidently a mere question of convenience, wh ich 
in any such case we fix on as the Characteristic of the 
Species we are contemplating. And either the one arrange- 
ment, or the other, may be the more suitable, according 
to the kind of pursuit we may be engaged in. 

An Agriculturist, for instance, (see Lesson VIII. § 5), 
would not characterize each kind of plants in the same 
way as a Botanist, or again, as a Florist ; no more would 
a Builder and a Geologist, and a Chemist, characterize in 
the same way the several kinds of stones. 



106 supplement. [Part III. 

§ 3. Any Predicable which belongs to some (and not to 
other) individuals of the same Species, [or which "may 
be present or absent, the Species remaining the same,"] 
is called an "Accident." 

And these are of two kinds. A "Separable-accident" is 
one which may be removed from the Individual; [or, which 
may be absent or present, in that which we regard as one 
and the same individual;] as, for instance (in an example 
formerly given), the "Sun" is regarded as the same indivi- 
dual thing, whether "rising," or "setting" or in any other 
situation relatively to the spot we are in: "rising," there- 
fore, or, "setting" are separable accidents of the Sun. 

So also, to be in this or that dress or posture, would be 
a separable-accident of an individual man; but to be a 
native of France, or of England, or to be of a certain 
eharacier, would be "inseparable-accidents." 

It is by inseparable accidents that we commonly distin- 
guish one Individual from another of the same Species, 
and to enumerate such accidents is called "giving De- 
scription" (See below, § 10.) 

Of course it is only from individuals that any "Accident" 
can be "inseparable;" for anything that is inseparable from 
a Species, [or, which forms a part of the signification of a 
Term by which we denote a certain Species,] is not an 
Accident, but a Property. 

§ 4. Some writers enumerate among Properties such Pre- 
dicates as are peculiar but not universal; that is, which 
do not apply each to every individual of a certain species, 
but are peculiar to that species, as Man alone can be "vir- 
tuous," — can be a "philosopher," &c, which are attributes 
not belonging to man. But these are more correctly reck- 
oned Accidents, though Accidents peculiar to the Species. 

Some again speak of " Properties" which are universal 
but not peculiar ; as "to breathe air" belongs to the whole 
human species, but not to that species alone. Such a 
Predicable however is not, strictly speaking, a Property of 
the Species "Man," but a property of a higher [more com- 
preJiensive] Species, "land-animal;" which stands in the 
relation of "Genus" to the species "Man." And it would 
be called accordingly, in the language of some writers, a 
"^e^eric-property of Man." A Property, strictly so 



Lesson iv.] division. 107 

called, of any Species under our consideration, would be 
called its "sj9eci/&c-property." 

Predicables then nave been usually divided into these 
five heads: " Genus, Species, Difference, Property, and 
Accident." 

You are to remember, that as every Predicable is so called 
in relation to the Terms of which it can be (affirmatively) 
predicated, so, each Common-term is to be regarded as 
belonging to this or that Head of Predicables, according 
to the Term to which it is in each instance applied, or 
which may be applied to it. Thus the term "Iron-ore" is 
a Species in respect of the term "Mineral/' and a Genus in 
respect of the term " Magnet ;" and so in other instances. 

§5. When we "enumerate distinctly" [or "separately"] 
the several things that are signified by one Common-term, 
— as the several Species included under some Genus — we 
are said to "divide" that Common-term. Thus, "natural- 
productions" are divided into "'Animal, Vegetable, and 
Mineral ;" and each of these again may be subdivided into 
several "members;" and so on. 

Perhaps the word "distinguish" if it had been originally 
adopted, would have been preferable to "divide-" (which, 
however, has been so long in general use in this sense, 
that it could not now be changed;) because "Division" 
being (in this sense) a metaphorical word, the "Division" 
we are now speaking of is liable to be confounded with 
"Division" in the other (which is the original and proper) 
sense of the word. 

"Division," in its primary sense, means separating from 
each other (either actually, or in enumeration) the parts of 
which some really-existing single object consists: as when 
you divide "an animal" (that is, any single animal) into its 
several members ; or again, into its "bones, muscles, nerves, 
blood-vessels," &c. And so, with any single Vegetable, &c. 

]N"oweach of these parts into which you thus "physically" 
(as it is called) divide "an animal," is strictly and pro- 
perly a "part," and is really less than the whole; for you 
could not say of a bone, for instance, or of a limb, . that it 
is "an Animal." 

In the very same sense, we divide any Group ["Class"] 
of objects, by separating (actually or mentally) those 



108 SUPPLEMENT. [Part III. 

objects from each other; as, when all the Cattle on a farm 
are divided into cows, horses, sheep, &c, or again, when 
the horses are divided, that is, placed separate from each 
other. Each horse is, here, actually less than "ail the 
horses;" and again, all the horses, less than "all the Cattle." 
But we commonly designate each Group [or Class] by a 
term that is applicable not merely to the whole Class col- 
lectively, but to each one of the objects thus placed to- 
gether: as, for instance, the term "'Metal" may be applied 
not only to all the Metal that exists, but to any kind of 
Metal, and to any portion of each kind; and so also 
" Iron" may be applied not only to all the Iron existing, 
but to any individual piece of Iron. 

And hence men have been led to employ the word 
"divide" metaphorically, (as has been said above,) in 
reference to the term itself which denotes a Class; as, 
when we speak of dividing "Metal" — that is the Genus 
"Metal"— into Gold, Silver, Iron, &e., or "Animal"— 
that is, the Genus "Animal" — into Beast, Bird, Fish, &c. 

Now when you thus — in the secondary sense of the word 
— "divide" a Genus, — that is, the term denoting a Genus, 
— each of the parts [or "members"] is metaphorically 
called a "'part," and is, in another sense, more than the 
whole [the Genus] that is thus divided. For you may say 
of a Beast or Bird that it is an "Animal;" and the term 
"Beast" implies not only the term "Animal" but something 
more besides; namely, whatever "Difference" characterizes 
" Beast" and separates it from " Bird," " Fish," &e. 

And so also any Singular-term [denoting one individual] 
implies not only the whole of what is understood by the 
Species it belongs to, but also more; namely, whatever 
distinguishes that single object from others of the same 
Species: as "London" implies all that is denoted bythe term 
" City" and also its distinct existence as an individual city. 

§ 6. The "parts" ["members"] in that figurative sense 
with which we are now occupied, are each of them less 
than the whole, in another sense; that is, of less comprehen- 
sive signification. Thus the Singular-term " Romulus" 
embracing only an individual king, is less extensive than 
the Species "King;" and. that, again, less extensive 
than the Genus " Magistrate," &c. 



Lesson xv.] division. 109 

An "individual" then is so called from its being incapable 
of being (in this figurative sense) divided. 

And though the two senses of the word "Division" are 
easily distinguishable when explained, it is so commonly 
employed in each sense, that through inattention, confu- 
sion often ensues. 

We speak as familiarly of the ''division" of "Man" 
(meaning Mankind) into the several races of "Europeans, 
Tartars, Hindoos, Negroes," arc, as of the "division" of the 
Earth into "Europe, Asia, Africa," &c., though "the Earth" 
[or "the World"] is a singular term, and denotes what we 
pall one Individual. And it is plain, we could not say of 
Europe, for instance, or of Asia, that it is a "World." But 
we can predicate '"Man" of every individual European, 
Hindoo, ivc. 

And. here observe, that there is a common colloquial in- 
correctness (increasing the liability to confusion) in the 
use of the word "division" in each of these cases, to denote 
one of the '''parts' into which the whole is divided. Thus 
you will sometimes hear a person speak of Europe as one 
"division" of the Earth : or of such and such a "division" 
of an Army : meaning "portion." And so again a person 
will sometimes speak of "animals that belong to the 
feline division of the Carnivora " [flesh eating animals] 
meaning that portion of the Class " Carnivora." 

§ 7. Division, in the sense in which we are here speak- 
ing of it, (the figurative.) is evidently the reverse process 
to "CTeneralization." (See Lesson VII. § d.) For as, in 
generalizing, you proceed by laying aside the differences 
between several things, and abstracting that which is com- 
mon to them, so as to denote them, — all and each, — by 
one Common-term, so, in dividing, you proceed by adding 
on the differences, so as to distinguish each by a separate 
term. 

When you take any Common-term to be divided and sub- 
divided, for any purpose you have in hand, — as, the Term 
"Animal" in a work on zoology — that term is called your 
"Summum [highest] genus," the several Species into which 
yon proceed to divide it, and which are afterwards divided 
each into other Species, are called, each of them, a " Sub- 
altern" Species or Genus; being, each, a Species in relation 



110 supplement. [Part III. 

to that which can be predicated of it, and a Genus in re- 
lation to the Species of which it can be predicated. 

Thus ''Iron-ore" (in the example lately given) is a Sub- 
altern Species, or Genus in relation to " Mineral" and to 
"Magnet" respectively. 

Any Species that is "not made a Genus of any lower 
Species/' in the division you happen to be engaged in, — 
or, in other words, which is not regarded as any further 
divisible except into individuals, — is usually called (by the 
Latin name) "infima Species;" that is, the "lowest Species." 

" Proximnm Genus" is a technical name often used to 
denote th.Q "Genus-next-above" [or " nearest,"] the Species 
you may be speaking of; as "Iron-ore" would be the 
"nearest" [proximum] Genus, of Magnet; and " Mineral" 
would be its more remote Genus ; that is, the Genus of its 
Genus. 

§ 8. It is usual, when a long and complex course of 
Division is to be stated, to draw it out, for the sake of 
clearness and brevity, in a form like that of a genealogical 
"Tree." And by carefully examining any specimen of 
such a "Tree" (going over it repeatedly, and comparing 
each portion of it with the explanations above given) you 
will be able perfectly to fix in your mind the technical 
terms we have been explaining. 

Take for instance as a '•Sunrmuin-Genus" the mathema- 
tical term. 

" Plane-superficial-figure." 

i 

i i I 

Mixed Fio-ure Rectilinear Figure Curvilinear Figure 



(of Rect. and Curv.) 



I 



Triangle Quadrilateral, &c. Circle Ellipse, <fec. 

Such a " Tree of division" the student may easily fill up 
for himself. And the employment of such a form will be 
found exceedingly useful, in obtaining clear views in any 
study you are engaged in. 

For instance, in the one we have been now occupied 
with, take for a Summun-Genus, " expression ;" (i.e., 
". expression-in-language" of any such mental-operation 
as those formerly noticed ;) you may then exhibit, thus, 
the division and subdivision of — 



Lesson xv.] 



TREE OF EXPRESSION. 



Ill 



n3 ea 

6^ 



~ ^ .rP 



O 5: 


fa ~*^ 


° S 

8.| 


in 


E 3> 

d 


| o 


"3 

fa 


s" 4 







^ ^ c s 



c ^ 

&>>.2 



112 supplement. [Part III. 

§ 9. The rules for dividing correctly are, 

i. That the Whole [or Genus-to-be- divided] be exactly 
equal to all the parts [or Members] together. Nothing 
therefore must be included of which the Genus can not 
be (affirmatively) predicated; — nothing excluded, of which 
it can. 

ii. The Members [Parts] must be "contradistinguished," 
(or, as some writers express it, "opposed,") and not include 
one another ; which they will do if you mix up together 
two or more kinds of division, made by introducing several 
distinct classes of differences. 

Thus, if you were to divide "Books" into "Ancient, 
Modern, Latin, French, English, Quarto, Octavo, Poems, 
Histories," &c., (whereof a "modern-book" might be 
"French," or "English"— a "Poem," or a "History," 
&c., a " Quarto-book," "ancient" or "modern," &c.,) you 
would be mixing together four different kinds of divisions 
of Books ; according to their Age, Language, Size, and 
Subject. 

And there are what are called Cross-divisions ; (because 
they run across each other, like vertical and horizontal 
sections of anything;) being divisions formed according 
to "distinct classes of Differences:" or, in other words, 
"on several distinct principles of division." 

It is a useful practical rule, whenever you find a discus- 
sion of any subject very preplexing and seemingly con- 
fused, to examine whether some "Cross-division" has not 
crept in unobserved. Por this is very apt to take place : 
(though of course such a glaring instance as that in theabove 
example could not occur in practice:) and there is no more 
fruitful source of indistinctness and confusion of thought. 

When you have occasion to divide anything in several 
different ways, — that is, "on several principles-of-di vision" 
— you should take care to state distinctly how many divi- 
sions you are making, and on what principle each proceeds. 

For instance, in the "Tree" above given, it is stated, 
that "Propositions" are divided in different ways, "as- 
cording to" this and that, &c. And thus the perplexity of 
Cross-division is avoided. 

§ 10. iii. A division should not be "arbitrary ;" that is, 
its Members should be distinguished from each other by 



Lesson xy.] definitions. 113 

" Differences" (see above, § 7.) either expressed or readily- 
understood ; instead of being set apart from each other at 
random, or without any sufficient ground. For instance, 
if any one should divide "coins" into " gold-coins," "silver," 
and "copper," the ground of this distinction would be in- 
telligible: but if he should, in proceeding to subdivide 
silver coin, distinguish as two branches on the one side, 
"shilling," and on the other, "all silver-coins except shil- 
lings," this would be an arbitrary Division. (See below ? 
§ 13.) 

iv. A Division should be clearly arranged as to its 
Members : that is, there should be as much subdivision as 
the occasion may require : and not a mere catalogue of the 
"lowest-Species," omitting intermediate classes ["subaltern"] 
between these and the " highest -genus :" nor again an in- 
termixture of the "subaltern" and "lowest species," so 
as to have, in any two branches of the division, Species 
contradistinguished and placed apposite, of which the 
one ought naturally to be placed higher up [near the 
" Summum"] and the other lower doivn in the Tree. 

For instance, to divide "plane-figure" at once, into 
'equilateral triangles, squares, circles, ellipses," &c, or 
again "vegetable" into "elms, pear-trees, turnips, mush- 
rooms," &c, or again to divide "Animal" into "Birds, 
Fishes, Reptiles, Horses, Lions," &c, would be a trans- 
gression of this rule. 

And observe, that (as was formerly remarked), 
although such glaring cases as are given by way of 
examples could not occur in practice, errors precisely 
corresponding to them may and often do occur; and 
produce much confusion of thought and error. 

§ 11. When you state the Genus that any Species be- 
longs to, together with the Difference that constitutes it 
["characterizes" it, so as to separate it from the rest], 
you are said to give a "Definition" of that species. 

As " the Magnet," (meaning a natural-magnet, is) 
defined "an iron ore, having an attraction for iron:" a 
" Triangle," a "three-sided figure:" a " Proposition," an 
"indicative," [affirming or denying] " Sentence," " Iron- 
ore" — " Figure" — " Sentence" are evidently each of the 



114 supplement. [Part III. 

Genus, in these definitions respectively; and the other 
part the Difference. 

This is accounted the most perfect and proper kind of 
Definition. And the two portions of which it consists — 
the "Genus" and the "Difference" are called technically 
the "metaphysical parts:" as not being two real parts 
into which any individual object can be actually divided, 
but only different views taken [or notions formed] of a 
Class of objects, by our mind. 

What is called a " physical-definition" is made by an 
enumeration of such parts of some object as are actually 
separable; such as are the Subject, Predicate and Copula 
of a Proposition; the root, trunk, branches, bark, <fce. of 
a Tree; &e. 

A Definition which proceeds by enumerating several 
Properties, — or — in the Case of an Individual — Insepa- 
rable-accidents ; is called a " Description ;" or, according to 
some writers, an "Accidental-Definition." 

It is evident, that an Individual can be defined only by a 
Description; that is, by stating the Species and (not "Pro- 
perties;" since they belong to all the individuals of the 
Species; but) the Inseparable accidents. As "Alexander 

Sp. 



the Great" would be described as "a Kimr" . . "of Mace- 

Sp. 

don, who subdued Persia ; " "Paris," "The capital . . City 
... of France - " 

§ 12. Definitions have also been distinguished — accord- 
ing to the object designed to be effected by each — into 
"Nominal" and "Real." 

A Nominal-definition is usually described as being one 
which explains merely the meaning of the word defined ; 
and a Real-definition, that which explains the nature oj 
the thing signified by that woi'd. 

Now it may naturally occur to you to ask, are not these 
(at least in defining a common-term) the same thing? 
since the object of our thoughts when we employ a 
Common-term is (see above, Lesson vii. § 7) — not any 
such really-existing-thmg as those imaginary abstract- 



Lesson xv.] rules for defining. 115 

ideas speak of, but, — the Term itself, regarded as a 
"Sign,'' arc, as was formerly explained. 

And in many cases, accordingly, the "Nominal" and the 
"Real" Definition do coincide. But by a u JTominal-deii- 
nition, is meant (strictly speaking), one which expresses 
exactly what the Name itself conveys to every-one who 
understands that name : and nothing beyond this. And 
any Definition may be called (in a greater or less degree) 
a i?ea?-definition which explains anything — more or less, 
— beyond what is necessarily implied in the Name itself. 

Thus, any one who gives such an account of some one 
of the '"metals" for instance, or of the " Sun," as modern 
researches would enable him to give, would be advancing 
beyond a mere Nominal-definition; since, in this latter, — 
the mere explanation of the words "iron" or "sun" — we and 
our ancestors 500 years ago, would coincide; since both they 
and we use those words in the same sense; though they 
knew much less than we do of the nature of those things. 

In the case of stiictly-scie^}ic-ternis, the Nominal and 
the Seal- definition may be regarded as coinciding. Thus, 
the mathematical-definition of a Circle, may be considered 
as strictly "Nominal," inasmuch as it denotes precisely the 
same as the word "Circle," and nothing beyond; every 
name being (in Mathematics) regarded as merely the "de- 
finition abridged." And again, it may be regarded as so 
far a "itea7-definition," that it conveys all that can belong 
to the thing spoken of, since there can be no property of 
a Circle that is not in fact implied in the definition of a 
Circle: or, which is the same thing, in the name, "Circle." 
It is therefore as much of a real-definition as can conceiv- 
ably be given of a Circle. 

And so with other scientific-terms. In respect of these, 
in short, the meaning of the name, and the nature of the 
thing, are one and the same. 

And accordingly, in Mathematics, the definitions are 
the Principles from which our reasonings set out. 

On the other hand, since a "diamond," or a "planet," 
or a " sheep," &c, have each of them (that is, each indivi- 
dual of any such Species) a real, actual existence in nature, 
independently of our thoughts, any of these may possess 
attributes not implied in the meaning we attach to the 



116 supplement. [Part III. 

name; and which are to be discovered by observations 
and experiments. Any explanation, however, of the nature 
of any object beyond what is implied in the signification of 
its name, is not usually called a " Definition; but the word 
" Description" is often used to denote such an explanation. 

§ 13. What we are concerned with at present is 
" Nominal-definition;" it being important with a view to 
Reasoning, to ascertain the exact sense in which each 
Term is employed, and especially to guard against any 
ambiguity in the Middle-term of an Argument. 

The rules [or cautions] commonly laid down in various 
treatises for framing a Definition, are very obvious: namely, 

i. That a Definition should be "adequate;" i. e., com- 
prehending neither more, nor less, than the term to be 
defined. For instance, if in a definition of " Money" you 
should specify its being " made of metal," that would be 
too narrow, as excluding the shells used as money in some 
parts of Africa : it again you would define it as an " article 
of value given in exchange for something else," that 
would be too wide, as it would include things exchanged 
by barter ; as when a shoemaker who wants coals, makes 
an exchange with a collier who wants shoes.* 

And observe, that such a defect in a Definition cannot 
be remedied by making an arbitrary exception; (such as 
was alluded to above, § 10;) as if for instance and it is 
an instance which actually occurred) a person should give 
such a Definition of " Capital" as should include (which 
he did not mean to do) "Land;" and should then propose 
to remedy this by defining "Capital" any "property of 
such and such a description except Land" 

ii. The other caution usually given, is, that a Defini- 
tion should be clearer than the Term defined : clearer, 
that is, to the persons you are speaking to : since that may 
be obscure to one man which is intelligible to another. 

And this rule evidently includes (what some give as a 
third rule) a caution against excessive prolixity, excessive 
brevity, and ambiguous language. 

* See Lesson I. on Money Matters. 



117 

PART IV. 

FALLACIES. 



LESSON XYI. 



§ 1 . Although sundry kinds of Fallacies have been from 
time to time noticed in the forgoing Lessons, it will be 
worth while to make some further observations thereon. 

By a " Fallacy" is commonly meant " any deceptive 
argument or apparent argument, whereby a man is him- 
self convinced — -or endeavours to convince others — of 
something which is not really proved." 

Fallacies have been usually divided into two Classes ; 
those in the form, and those in the matter : though the 
difference has not been in general clearly explained. 

The clearest way of proceeding will be to consider a 
" Fallacy-in-form" as one in which the Conclusion does 
not really follow from the Premises ; and a " Fallacy-in- 
matter" as one where the Conclusion does follow from 
the Premises, though there will be still something faulty 
in the procedure. 

In this latter case (where the Conclusion does follow) 
one may either object to the Premises as being " unduly- 
assumed," or to the Conclusion as irrelevant; that is, 
different, in some way, from what ought to have been 
proved — -namely, from what was originally maintained, — 
from what had been undertaken to be established, — from 
what the particular occasion requires ■ &c. 

These that have been mentioned (as the " Fallacies-in- 
form," and "in matter") must evidently include every 
possible Fallacy * since whatever objection can be brought 
against any argument, or apparent argument, must be an 
objection either against the Conclusion, or against the 
Premises, or against the connexion between the premises 
and conclusion ; that is, against the conclusiveness of the 
apparent argument. 

§ 2. " Fallacies-in-form," [in which the Conclusion does 
not really follow from the Premises] are such as we have 



118 fallacies. [Part IV. 

already given examples of, as violations of the rules above- 
explained : such as "undistributed-middle/' — "illicit-pro- 
cess," &c. 

Among others was noticed the fault of an " equivocal 
Middle-term," taken in one sense in the one premise, and 
in a different sense in the other. And since this Fallacy 
turns on the meaning of words, and not on the mere form 
in which the argument is expressed, some may be disposed 
to rank it rather under the Head of" Fallacies-in-raatter." 

The most convenient course, however, will be to keep to 
the division already laid down ; and, accordingly, to reckon 
the Fallacy of "equivocal-middle" along with all the others 
in which the conclusion does not follow from the Premises. 

And, in truth, the technical rules do apply to this' — the 
"Fallacy of equivocation" — as soon as it is ascertained that 
the Middle-term is employed in two different senses, and 
consequently is, in reality, not one, but two terms. 

But of course the rules of Syllogism do not, alone, 
enable us to ascertain the meaning or meanings of any 
Term. That must be judged of from our knowledge of 
the subject-matter, — from the context, [or general drift of 
the discourse] — and often from what we know or believe 
concerning the writer or speaker. 

And the same may be said, in many cases, in respect of 
not only the signification, but also the distribution or non- 
distribution, of a Term ; on which depend the fallacies of 
"undistributed-middle" and "illicit-process." For when 
a Proposition is expressed indefinitely (as " Man invents 
arts ;" " Man is mortal ;") we are left to judge from the 
subject-matter, (fee, whether it is to be understood as 
Universal or as Particular. 

And again, the sign "all," (which in an Affirmative-pro- 
position, denotes Universality) in a Negative-proposition, 
generally, though not invariably, indicates a Particular ; 
that is, usually, though not always, the negation is under- 
stood as a negation of universality. For instance, of these 
two propositions, " all they that trust in Him shall not be 
confounded," and " we shall not all sleep," the one would 
be understood as Universal, and the other, as Particular. 

Observe also that the sign "all" is sometimes under- 
stood as meaning "ail-collectively;" sometimes "every-one, 



Lesson xvi.] equivocation. 119 

separately" As " all the apples on that tree are enough 
to nil a bushel ;" i.e. 3 all together ; and " they are a^ripe;" 
i. e., every one. 

If this ambiguity be overlooked, two propositions, both 
true, may appear to be Contradictories. For instance, " All 
these apples are worth twenty shillings •" and " Some of 
these apples are not worth twenty shillings." The right- 
contradictory would be "All these apples together are 
not worth twenty shillings." 

There is an ambiguity answering to this, in the word 
" some," which ocasionally means " some definite one," 
and occasionally, " either one or else another." For in- 
stance, if I say " some food is vegetable," I mean that 
" there actually exists some kind of vegetable food ;" and 
this being true, its contradictory, "no food is vegetable," 
must be false. But if I say " some food is necessary to 
life," the apparent contradictory, "no food is necessary to 
life," is, in a certain sense, true ■ for there is no one definite 
article of food of which it can be said that it is necessary 
to life. But some article of food or other is necessary ; which 
is the meaning of the original proposition ; and the real 
contradictory to it will therefore be, "all food is not neces- 
sary to life;" i. e., "life may be supported without any 
food at all." [See § 12 of this Lesson.] 

§ 3. You are to observe that we cannot always decide 
absolutely as to which Class we should pronounce some 
particular fallacy to fall under, those in "form" or those in 
"matter:" because it will often happen, when an argument 
is stated (which is usually the case) as an Enthymeme, that 
the suppressed premise may be either one which is false, 
but which would, if granted, make the Syllogism complete: 
or else one which is true, but which would not complete a 
regular Syllogism. Now, on the former supposition, the 
Fallacy would be in the "matter;" on the other supposition, 
it would be in the "form." 

For instance, in this Enthymeme, "The Country is dis- 
tressed ; therefore it is misgoverned," we cannot decide 
absolutely whether the premise meant to be understood, 
is, " every Country that is distressed is misgoverned ;" 
which would make the syllogism correct, but would not be 
admitted as true; or, every Country that is misgoverned 



120 fallacies. [Part IV. 

Is distressed ; which would leave the Middle-term undis- 
tributed. 

And again, when both Premises are expressed, it will 
often happen (as in an example formerly given) that we 
have the alternative of either denying the truth of one of the 
premises, — supposing the Middle-term used in the same 
sense in both — or denying the conclusiveness of the argu- 
ment, supposing the Middle-term used in each premise in 
such a sense as to make that premise true. If by" contrary 
to experience'' you mean two different things, in the two 
premises, respectively, then, each is, by itself, true, but 
they prove nothing : if you mean by it the same in both 
premises, respectively, then, one of them is untrue. 

§ 4. But observe, that when you mean to charge any 
argument with the fault of " equivocal-middle," it is not 
enough to say that the Middle- term is a word or phrase 
which admits of more than one meaning; (for there are 
few that do not;) but you must show, that, in order for 
each premise to be admitted, the Term in question must be 
understood in one sense (pointing out what that sense is) 
in one of the premises, and, in another sense, in the other. 

And if any one speaks contemptuously of "over-exact- 
ness" in fixing the precise sense in which some term is 
used, — of attending to minute and subtle distinctions, &c, 
you may reply that these minute distinctions are exactly 
those which call for careful attention; since it is only through 
the neglect of these that Fallacies ever escape detection. 

For a very glaring and palpable equivocation could never 
mislead any one. To argue that "feathers dispel darkness, 
because they are light" or that " this man is agreeable, 
because he is riding, and riding is agreeable," is an equivo- 
cation which could never be employed but in jest. And 
yet, however slight in any case may be the distinction 
between the two senses of a Middle-term in the two pre- 
mises, the apparent- argument will be equally inconclu- 
sive ; though its fallaciousness will be more likely to escape 
notice. 

Even so, it is for want of attention to minute points 
that houses are robbed, or set on fire. Burglars do not in 
general come and batter-down the front door; but climb 
in at some window whose fastenings have been neglected. 



Lesson xvi.] equivocation. 121 

And an incendiary, or a careless servant, does not kindle a 
tar-barrel in the middle of a room, but leaves a lighted turf, 
or a candle-snuff, in the thatch, or in a heap of shavings. 

In many cases, it is a good maxim, to " take care of 
little things, and great ones will take care of themselves." 

§ 5. Of the Fallacies of " undistributed-middle " and 
of " illicit-process," <fec, (which have been formerly ex- 
plained,) no more need be said in this place. 

But in respect to the " Fallacy of equivocation," it is 
worth while to notice briefly some of the different modes 
in which a word or phrase comes to be employed in 
several senses. 

i. That may be reckoned an accidental equivocation, in 
which there is no perceived connexion between the differ- 
ent senses. Thus " pen " is an instrument for writing, or 
an enclosure for cattle; " turtle" a kind of bird, and a 
kind of tortoise ; and " case " is used ( as was noticed in 
Lesson VII. § 3) in three senses. Of this kind is the am- 
biguity of several proper-names (as John, Thomas, &c.) 
also notified in the same place. 

ii. There are several words which are ambiguous from 
being employed in what is technically called a c first- 
intention 1 and a "second-intention." 

A " second-intention," of any word is that signification 
which it bears in reference to some particular art, science, 
study, pursuit, or system : and its first-intention is its or- 
dinary colloquial sense when there is no such reference. 

Thus the ordinary signification of the words "ship," 
"beast," and "bird," every one knows; but sailors limit 
the word "ship" to vessels of a certain construction; 
"beast" is the word applied by farmers in some parts, 
especially and exclusively, to the "ox-tribe;" and " bird" 
is used in a "second-intention" by sportsmen, to signify 
" partridge." 

§ 6. It is evident, that a word may have several dif- 
ferent " Second -intentions," according to the several 
systems &c. into which it may be introduced as one of 
the technical-terms. 

Thus, "line" is technically employed in Geometry, in 
Geography, in the Military-art, in the Art of Angling, 
in Printing, &c. 
F 



122 fallacies. [Part TV. 

The word "Species" is employed by Naturalists in a 
certain " Second-intention" when they are speaking of 
organized-beings. 

The ordinary sense ["first intention"] of the word, is 
that which has been explained in these Lessons; but 
Naturalists restrict it to such a class of animals or plants 
as are supposed to have descended from a common Stock. 

In ordinary discourse, any one would say that a " Grey- 
hound" or a "Mastiff" is a kind ["Species"] of dog; 
but a Zoologist would say (in technical language) that 
these are only " Varieties" and that all dogs are of one 
Species. So also, in common discourse, any one would 
speak of "Cauli-nower," and several others, as "kinds" 
of "Gabbage:" but the Botanist reckons all these as 
"varieties" of the single Species, Cabbage. 

Those, in short, which are (in the technical language 
of these Lessons) the "lowest-species" that the Naturalist 
treats of, are called by him, not Species, but Varieties; 
and, again, those classes under which his Species come, 
he never calls Species of a higher Genus, but Genera, 
Orders, &c. « 

Much confusion of thought has often arisen from over- 
looking this technical-sense ["second-intention"] of the 
word " Species." 

In some instances, the "second-intention" [or philoso- 
phical sense] of a word is, — instead of being more limited, 
— more extensive than the "first-intention" [or popular 
sense]. 

Thus "affection," which is limited, in popular use, to 
"love," is employed by philosophers as comprehending 
both "benevolent and malevolent affections." So also 
"charity," which is often, in popular use, confined to 
"almsgiving" — "flower," to such flowers as have conspi- 
cuous petals, — and "fruit," to such fruits as are "eatable," 
have each a technical second-intention, which is more 
extensive. 

§ 7. iii. A word will often be employed to denote (in • 
different senses) two things which have a "resemblance" 
or an "analogy" to each other. 

A "blade" of grass, or of & sword, have the same name from 
the direct resemblance between the things themselves. 



Lesson xvi.] analogy. 123 

But instances of this kind are far less common than those 
in which the same name is applied to two* things, not 
from their being themselves similar, but from their having 
similar relations to certain other things. And this is 
what is called " Analogy." 

Thus, the sweetness of a "sound" and of a "taste" can 
have no resemblance ; but the word is applied to both, by 
analogy, because as a "sweet" taste gratifies the palate, so 
does a "sweet" sound the ear. 

Thus also we speak in the "secondary" [or "transferred," 
or "analogical"] sense of the-" hands" of a Clock, — the "legs" 
of a Table, — the "foot" of a Mountain, — the "mouth" of a 
River, <fec; which words in their "primary" ["proper," or 
original] sense, denote the- "hands" of a man, — the "legs, 
foot, and mouth" of animals; from the similar relations 
in which they stand to other things respectively, in refe- 
rence to use, position, action, &c. 

The words pertaining to Mind may in general be traced 
up, as borrowed, (which no doubt they all were, originally) 
by Analogy, from those pertaining to Matter: though in 
many cases the primary sense has become obsolete. 

Thus " edify, "* in its primary sense of "buildup,"! 
is disused, and the origin of it often forgotten; although 
the substantive "edifice" remains in common use in a 
corresponding sense. 

When, however, we speak of "weighing" the reasons 
on both sides, — of "seeing" or "feeling" the force of an 
argument, — "imprinting" anything on the memory, &c, 
we are aware of these words being used analogically. 

It is in an analogical sense that "Division," "Part," 
and several other technical terms, have been employed in 
these Lessons. 

§ 8. There are two kinds of error — each very common 
- — which lead to confusion of thought in our use of ana- 
logical words: 

i. The error of supposing the things themselves to be 
similar, from their having similar relations to other things. 

ii. The still commoner error of supposing the Analogy 
to extend further than it does; [or, to be more complete 

* See 1 Peter ii. 5. f, See Johnson's Dictionary. 



124 FALLACIES. |T art ^V- 

than it really is;] from not considering in what the 
Analogy in each case consists. 

For instance, the "Servants" that we read of in the 
Bible, and in other translations of ancient books, are so 
called by Analogy to servants among ns : and that Ana- 
logy consists in the offices which a "servant" performs in 
waiting on his master, and doing his bidding. It is in this 
respect that the one description of "servant" "corresponds" 
["answers"] to the other. And hence some persons have 
been led to apply all that is said in Scripture respecting 
Masters and Servants, to these times, and this country: 
forgetting that the Analogy is not complete, and extends 
no further than the point above mentioned. For the 
ancient "servants" (except when expressly spoken of as 
hire ^-servants) were Slaves; a part of the Master's £>os- 
sessions. 

§9. iv. A word will often (in diffeient senses) be 
applied to two things, connected, not by Resemblance 
or Analogy, but by the circumstances of time or place, as 
being "Cause and Effect," or "Part and Whole," &c. 

Thus, when we say "wormwood has a bitter taste" and 
" I have a bitter taste in my mouth," it is plain that the 
" taste" of wormwood is not a sensation in wormwood, (as 
our taste is in us,) and cannot resemble or be analogous 
to a sensation; but is the cause of the "sensation" of 
" taste" in me. 

This kind of transfer of a word from its " primary" to 
a "secondary" sense, is called "Metonymy" It is thus we 
speak of a "Crown," or a "Throne," for " regal -power," 
"the sword," for "war;" a "voice" for a "declaration;" and 
a man is said to be "worth" such and such a sum of 
money ; meaning that he possesses p>roperty that is worth 
so much, ifec. 

Much confusion of thought, and many Fallacies, have 
arisen from inattention to this source of ambiguity. * It 
seems strange, but it is quite true, that things have often 
been in this way confounded together which have not the 
least Resemblance or Analogy to each other. 

* The ambiguity of the word "Division," when used to signify one of the 
portions into which anything is divided (see Lesson XV. § 6) is of this kind. 



Lesson xvi.] analogy. 125 

A remarkable instance of this is to be found in the 
" primary" and "secondary" uses of such words as "same" 
— "one" — "identical" &c. In the primary sense they 
imply "numerical unity" [individuality], and do not 
imply, necessarily, any similarity. For when we say of 
any grown man, that he is the " same person" whom we 
remember to have seen when an infant, that is not from 
his now resembling an infant. Another infant, now, would 
be much more like what he then was. 

In the "secondary" sense, on the other hand, these words 
imply nothing but exact — or nearly exact — similarity. For 
instance, if a man finds in a mine some metal which turns 
out to be gold with a small alloy of copper, he would say, 
it is the same metal of which coins, or of which watches 
are made ; or if he finds a stone which proves to be a 
diamond or ruby exactly such as he had seen in a certain 
ring, he would say, it is the same precious-stone as the one 
in that ring ; not meaning, of course, that — in the strict 
sense — " one and the same" metal or stone can be in two 
places at once ; but only that there is a perfect similarity. 

So, also, several persons are said to be in one and the 
same posture, when they are all placed alike; and to have 
"one and the same" idea in their minds, when they are 
all thinking alike. (See Lesson VII. § 8). 

§ 10. ISTow the mode in which these words have been 
thus transferred (to the utter bewilderment of the inatten- 
tive) is this : one single word,— such as "gold," or "man," 
or " triangle," or " fever," — will equally well apply to 
any one piece of gold, or individual man, or triangle, 
or fever, <fcc. And so, also, will one single Definition [or 
Description] of a triangle : and hence the things them- 
selves come to be called "one," — the "same" "identical," 
&c, because all the individuals thus named or described, 
are (according to the modern phrase, which is very correct) 
" of the same description." 

In the transferred [secondary] sense, accordingly, you 
may observe, that things are often spoken of as "very 
nearly the same, but not quite;" there being some small 
difference between them. In the " primary" sense, on 
the other hand, "unity" — " identity," &c, do not admit of 
degrees. For instance, "This man," either is or is not the 



126 fallacies. [Part IV. 

same person whom I saw formerly when he was an infant 
or child \ and that, whether he differ much or little, from 
what he then was. 

But what helps to introduce confusion is, that "identity" 
in the primary sense, is in many cases judged of, and "in- 
ferred" from similarity. For instance, a man may be ready 
to swear to some picture as the one which he had lost, 
from his perceiving a perfect similarity ; and yet it might 
perhaps be afterwards proved to his satisfaction, that it- 
was not that one, but an exact copy. 

§ 11. Besides the causes of ambiguity that have been 
just mentioned, it is to be observed that there are several 
words which it is customary to employ elliptically; that 
is, in combination with something understood ; and that 
men are apt to forget when it is that such a word is used 
with, and when without, this ellipsis. 

For instance, we speak of such a one possessing 10,000 
pounds; (though perhaps he may not actually possess 
ten pounds in money); meaning, that his whole property 
would exchange for that sum. And ordinarily, such a 
mode of speaking leads to no practical inconvenience. 
But there is no doubt that it has contributed to foster 
that enormous practical error known, among Political 
Economists,* as the " Mercantile System." 

So also we speak commonly of "the example of such a 
one's punishment serving to deter others from crime." And 
usually, no misapprehension results from this, which is, 
in truth, an elliptical expression. But sometimes sophis- 
tical reasoners take advantage of it, and men who are not 
clear-headed are led into confusion of thought. Strictly 
speaking, what deters a man from crime, in such cases as 
those alluded to, is the apprehension of himself suffering 
punishment. That apprehension may be excited by the 
example of another's being punished ; or it may be excited 
ivithout that example, if punishment be denounced, and 
there is good reason to expect that the threat wili" not be 
an empty one. And on the other hand, the example of 
others suffering punishment does not deter any one, if 
it fail to excite this apprehension for himself; if, for 

* See Senior's and Whately's Lectures on Political Economy. 



Lesson xvi.] ellipsis. 127 

instance, he considers himself as an exempt person, as is 
the case with a despot in barbarian countries, or with a 
madman who expects to be acquitted on the plea of 
insanity. 

So, also, when any one speaks of being in distress from 
being "out of work" and of his "seeking for employment" 
we understand him to mean "work by which he can earn 
a subsistence" But great errors have often been committed 
by writers who have lost sight of the elliptical character 
of the expression, till they have practically forgotten in 
their reasonings that the thing really desired is, not the 
labour but the gain. 

To this head may, perhaps, be referred the ambiguity 
(which has been a source of endless confusion) formerly 
noticed (Lesson II.) of such words as "because," &c, and 
again "therefore," and several others. 

When, in accounting for the wetness which I perceive 
on the ground, I say, "the ground is wet because it has 
rained, I mean (speaking at full length) to assign the 
" rain" as the "cause of the wetness :" when, again, I infer 
that "it has rained because the ground is wet," the mean- 
ing of the word "because" is, if fully expressed, that I 
assign the wetness as the " cause of my belief" 

The same may be said of such words as "may," "pos- 
sible," <fcc., and again, "must," "necessary," &c. (See 
Lesson X. § 8). 

When I say of a man forcibly carried off by enemies, 
"he must go wmerever they conduct him," I mean, "he 
cannot avoid going :" when I say that on his release "he 
onust eagerly return to his home," I mean that "I cannot 
avoid drawing that conclusion" 

So, also, if I say of a man in health and at liberty, " he 
may go out or stay within," I mean that neither going nor 
staying is unavoidable to him : but when I say of a man 
who is sick, that "he may recover," I do not mean (as 
in the former case) that "this depends on his choice" but 
that " I am not led unavoidably to the conclusion, that he 
will recover, or that he will not recover." 

§ 12. There are also other ways in which a Term may 
be so modified in its sense as not to have precisely the 
same meaning in. both premises. 



128 fallacies. [Part IV. 

For you are to remember that even any one word which 
is not itself one of the terms, but only a small portion of 
one of them, may be so understood as to affect the sense 
of the whole Term. Even a difference in the position 
of a word in respect of the rest, may greatly alter the 
sense. 

For instance, "He who believes his opinion always 
right deems himself infallible : you always believe your 
opinion right ; therefore you deem yourself infallible. " 
Here, the premises are both true ; for any opinion which 
you did not believe to be right, would plainly not be your 
opinion ; and it would be difficult to deny that a man 
considers himself infallible, who should believe that his 
opinion is invariably right. But the different situation of 
the word "always" gives a different sense to the Middle- 
term in the two premises. To " think your opinion always 
right," means, to have a general conviction respecting the 
whole of your opinions collectively, that none of them is 
ever wrong ; but " always to think your opinion right," 
means, "to have a particular conviction, on each occasion, 
separately ', that your opinion on that occasion is right." 

A Fallacy of this character — that is, where the Middle- 
term is taken collectively in one premise, and clivicledly in 
the other, — is technically called the "Fallacy-of-cZ^moft," 
or of " composition ;" according as the Middle-term is un- 
derstood in a collective-sense in the J/cyVr-preniise, and in 
a divided sense in the Minor; or vice versa. 

A glaring example would be, " all the apples from that 
tree are worth 20s. ; this is an apple from that tree ; 
therefore it is worth 20s." 

Such a fallacy has helped to give plausibility to what 
has been called " the doctrine of necessity." For instance, 
"He who necessarily goes or stays" (in reality, "who 
necessarily goes, or again, who necessarily stays") is not 
a free-agent; you necessarily go or stay; (that is, — 
taking these two things in connexion, — you " necessarily 
take the alternative ;") " therefore you are not a free- 
agent." 

§ 13. The way in which this Fallacy usually occurs in 
practice, is, when something is proved separately concern- 
ing each one of several things belonging to some class ; and 



Lesson xvi.] fallacies-of-division. 129 

then this is considered as having been proved concerning 
the whole class collectively •; that is, concerning those things 
taken in connexion with each other. 

A man, for instance, swallows a certain drug, and is 
seized with alarming symptoms; you show that these 
symptoms may possibly have arisen from other causes ; the 
same drug is swallowed by another man, who is seized with 
like symptoms: and you show that other causes may have 
produced the symptoms in him; the same may be shown, 
suppose, in each separate case (considered each by itself) 
out of 100; and then you assume that it has been proved 
that all the men who have taken the drug and exhibited 
like symptoms may have been affected, all of them, by 
natural causes. 

This kind of argument has been employed to refute the 
accounts given by the Evangelists of the miracles they 
record ; that is, explaining some one of the recorded cures 
— considered by itself, as an accident ; and then the same 
with another, and another; and so on. 

Sometimes again a Middle-term is ambiguous from being 
understood in one premise in conjunction uHtk certain cir- 
cumstances actually pertaining to it, at a particular time, 
&c, and in the other premise, independently of those cir- 
cumstances. A glaring example would be, if any one 
should pretend to prove (which of course would be only 
as a jest) that because what you have on your back was 
the covering of a sheep, therefore the sheep wore a coat 
of blue or red broadcloth. This is called in the technical 
language of the Latin treatises " Fallacia accidentis " 

It is evident that when any ambiguity, of whatever kind, 
in a Middle-term, is suspected, the natural course is to seek 
for, or to demand, a Definition of it. Only, remember 
that it would be impertinent to insist, in every such case, 
on a complete definition, beyond what is requisite for re- 
moving any doubt as to the argument before us; i. e. as to 
the Middle-term's being employed in the same sense in 
both premises. 

For instance, if there were a discussion respecting a 
person's having swallowed "poison" and some ambiguity 
connected with the reasoning, were suspected in the 
employment of the word, it would not be necessary to 



130 fallacies. [Part IV. 

give a definition such as should extend to " every poison," 
including such as savages use for their arrows: because 
the supposed question relates only to poisons taken into 
the stomach. 

§ 14. The Fallacies -in-matter are divided (as has been 
said) into two kinds: u undue-assumption-o fa-premise" 
and "irrelevant conclusion. 11 

It is to be observed that no one is to be charged with 
fallacious-proceeding merely because he argues from Pre- 
mises which we deny; or because the Conclusion he draws 
is not the one we would wish to see proved. For neither 
of these implies any deception. 

One man may assume facts or principles which another 
will not admit; but provided he does this openly and 
knowingly, there is no Fallacy in the case. 

Or again, we may, (suppose) wish to have it pointed 
out and proved who is the perpetrator of such and such 
a crime; but if the accused party prove that it was not 
he, we have no right to demand more. 

But if any one is convinced by an argument based on 
some Premise which he would not have admitted if dis- 
tinctly put before him, there is in this case a Fallacy. 

And so there is, if any one is satisfied, or endeavours to 
satisfy others, by proving some conclusion, different from 
what he had originally maintained; or from what was 
originally proposed as the Question : or, (which comes to 
the same,) which is the contradictory, not, of what he had 
originally denied, but of some different proposition. This 
is properly the Fallacy of "irrelevant conclusion." 

§ 15. Under the former of these two classes of Fallacy 
comes what is, technically, called "begging the Question;'* 
that is, assuming as a Premise the very proposition which 
— in other words — is proved as the Conclusion. The way 
in which this is usually done is that which is commonly 
called, "arguing in a Circle;" that is, proving some con- 
clusion by means of a Premise which is itself deduced — - 
more or less remotely — from premises deduced from that 
very Conclusion, assumed as a premise. As if you were 
to prove that A is B, because C is D; and that C is D, 
because E is F; and so on, till at length you come to infer 
that Y is Z because A is B. 



Lesson xvi.] fallacies-in-matter. 131 

Of course the narroiver the Circle, the less likely it is to 
escape the detection, either of the reasoner himself, (for 
men often deceive themselves in this way,) or of his hearers. 
When there is a long circuit of many intervening proposi- 
tions before you come back to the original Conclusion, it 
will often not be perceived that the arguments really do 
proceed in a "Circle." Just as when any one is advancing 
in a straight line (as we are accustomed to call it) along a 
plane on this Earth's surface, it escapes our notice that we 
are really moving along the circumference of a Circle, (since 
the earth is a globe,) and that if we could go on without 
interruption in the same line, we should at length arrive 
at the very spot we set out from. But this we readily 
perceive, when we are walking round a small hill. 

For instance, if any one argues that you ought to submit 
to the guidance of himself, or his leader, or his party, &c, 
because these maintain what is right; and then argues that 
what is so maintained is right because it is maintained by 
persons whom you ought to submit to ; and that these are 
himself and his party; or again, if any one maintains 
that so and so must be a thing morally wrong, because it 
is prohibited in the moral portion of the Mosaic-law, and 
then, that the prohibition of it does form a part of the 
moral (not the ceremonial, or the civil) portion of that 
Law, because it is a thing morally wrong, — either of these 
would be too narrow a Circle to escape detection, unless 
several intermediate steps were interposed. And if the 
form of expression of each proposition be varied every time 
it recurs, — the sense of it remaining the same — this will 
greatly aid the deception. 

Of course, the way to oppose the Fallacy, is to reverse 
this procedure: to narrow the Circle by cutting off the 
intermediate steps: and to exhibit the same proposition, — 
when it comes round the second time, — in the same words. 

§ 16. In all cases, an unduly-assumed premise, (i.e. one 
which would not be admitted if clearly stated, and delibe- 
rately considered,) is the more likely to escape detection, 
the longer the train of argument is, and the greater the 
number of well- established propositions introduced. — 
When this artifice is employed, a dull or thoughtless hearer 
is apt to say "there is much truth in what has been urged," 



132 fallacies. [Part VI. 

And so perhaps there is. There may have been intro- 
duced, in the course of the reasoning, twenty propositions, 
all of them true, except one; the denial of which one would 
nullify the whole train of arguments. A chain which 
has only one faulty link, is not indeed the stronger, but 
is the more likely to appear strong, by the addition of a 
great many sound links 

It also contributes to this kind of deception, to suppress 
the unduly-assumed premise; stating the argument as 
an Enthymeme expressing the true premise, and giving 
proofs of the truth of that, as if everything turned on the 
establishment of that premise. 

So also, in Fallacies of the other class, — the "irrelevant- 
conclusioii" — it often aids the deception, to suppress the 
Conclusion itself : bringing forward arguments which do 
indeed go to prove a Conclusion, somewhat like the one 
required, though not the very one: and then (instead of 
expressly stating the Conclusion that really does follow, 
or again, that which had been originally maintained) a 
man will say, "the inference from this is plain;" or "I 
have thus established my point;" or "the position of our 
opponents is thus completely overthrown," &c. 

§ 17. The two kinds of " Fallacy -in-matter," are very 
commonly combined in one course of argument : that is, 
a false or a doubtful premise will be assumed as having 
been proved by arguments which go to prove, not that, 
bu'o another proposition, somewhat like it. 

For instance, instead of proving that "this Prisoner has 
committed an atrocious fraud," you prove that "the fraud 
he is accused of is atrocious:" instead of proving (as in 
the well-known tale of Cyrus and the two coats) that " the 
taller boy had a right to force the other boy to exchange 
coats with him," you prove that " the exchange would 
have been advantageous to both;"*instead of proving that 
"a man has not the right to educate his children, or to 
dispose of his property, in the way he thinks best," you 
show that the way in which he educates his children, or 
disposes of the property, is not really the best; instead of 
proving that " the poor ought to be relieved in this way 
rather than in that," you prove that the poor ought to be 
relieved; instead of proving that "an irrational-agent — 



Lesson xvi.] fallacy-in-matter. 133 

whether a brute or a madman — can never be deterred 
from any act by apprehension of punishment," (as for 
instance a dog, from sheep-biting, by fear of being 
beaten,) you prove that "the beating of one dog does 
not operate as an example to other dogs, &c. ; and then 
you proceed to assume as premises, conclusions different 
from what have really been established. 

The chief difficulty in detecting any Fallacy of what- 
ever kind in our own reasonings, or another's, arises (as 
was formerly remarked) from its being usually stated in an 
oblique, indirect and somewhat inverted and perplexed 
form of expression ; and more especially when diluted, 
as it were, with a multitude of words ; just as poison 
is more likely to escape detection, when disguised and 
diluted by being mixed up with a quantity of innocent 
ingredients, than when presented in a small concentrated 
dose. 

The validity, or the fallaciousness, of any course of 
reasoning, will then be made the most evident, when 
examined according to the forgoing rules, after laying 
aside all redundant words put in for mere embellishment 
of style, and stating the whole in the most simple lan- 
guage, and in regular order, as briefly as is compatible 
with perfect clearness. 



134 

PART Y. 
DIFFERENT KINDS OF ARGUMENT. 



LESSON XVII. 



§ 1. It remains to make a few remarks on the u finding 
[according to the Latin writers, Invention] of arguments ;" 
the foregoing Lessons relating only to the rules for passing 
judgment on arguments. 

It is to be observed in the first place, that the words 
"infer" and "prove" (which we have frequently had occa- 
sion to employ,) denote, not two different things, but the 
same thing considered in two different points of view. He 
who "infers" (correctly) proves; and he who "proves" 
infers : and yet the two expressions are not synonymous. 

So also, the "road from London to Liverpool" and 
the "road from Liverpool to London," are not different 
things ; but the one expression calls to the mind the* 
thought of a journey fro m the Metropolis to the Seaport; 
and the other, the reverse. And in like manner, the 
word "infer" fixes the mind first on the Premises and then 
on the Conclusion ; the word " prove," on the contrary, 
leads the mind from the Conclusion (in this case called 
the " Question") to the Premises. 

Hence, we say commonly "What do you infer from that]" 
"How do you prove this?" namely, this Conclusion? 

And the corresponding Substantives are often used to 
denote that which is, in each instance, last in the mind : 
" inference " being often used to signify a Conclusion 
[Proposition-inferred] and "proof," a Premise. 

When then any long train of reasoning is carried on, we 
proceed — in "inferring," and in "proving" — in opposite 
directions: our object being, in the one case, to ascertain 
from all that we know on a certain subject, what Conclu- 
sion is to be drawn ; and in another case, — when we are 
satisfied as to the conclusion — to consider by what argu- 
ments we shall establish it. 



Lesson xvii.] different kinds of arguments. 135 

§ 2. In the former case, from established "data" [cer- 
tain known facts, and acknowledged principles] we infer 
so and so; and from this conclusion, in conjunction with 
other known truths, we infer something else ; and so on, 
till we have ascertained what is decisive of the question 
before us, or as much as we are able. 

In the latter case, we proceed upwards from the Premises 
which will establish the Conclusion we are maintaining, 
to the arguments which will prove those Premises: and 
so on, till we arrive at something that is admitted. And 
from this, — when we have to convince others — we gene- 
rally proceed through the same train of reasoning, in a 
reversed order, downioards, till we have arrived at the 
Conclusion to be established. 

We are sometimes then employed in what may be 
called "seeking for a Conclusion" and sometimes again, 
in " seeking for Middle-terms." 

For instance, a Judge is inquiring whether the estate 
does^ or does not, belong by law to the claimant : the Suitor 
(or his Advocate) is seeking for proofs that the estate is 
his. The Natural -philosopher, when in vestiga ting, inquires 
"what is the cause of the tides ;" the Physician "what 
is this patient's disease;" and each, when he has satisfied 
himself, and is proceeding to teach and to convince others, 
sets himself, — 4ike the Advocate — to seek for proofs: 
sometimes employing the same that had led himself to 
the conclusion, and sometimes different ones; according 
to what he judges will serve best to satisfy the under- 
standing of others, that " the cause of the tides is so and 
so ;" or that " such and such is the patient's disease." 

And thus, in laying before others this process of reason- 
ing, a man will sometimes proceed in the same order in 
which he had sought for the arguments, (that is, begin- 
ning from the Conclusion, and proceeding ujjwards,) or 
again, sometimes in the reverse-order; setting out from 
something that is admitted, and proceeding doionwards 
towards the ultimate Conclusion. * 

§ 3. In treating of the operation of seeking for Middle- 
terms — in other words, for Arguments to establish, on each 

* See the notice in Lesson IX. of the Analytical and Synthetical order. 



136 DIFFERENT KINDS OF ARGUMENTS. [Part V. 

occasion, the Conclusion maintained — we are naturally 
led to inquire concerning the different kinds of Arguments 
one often finds alluded to in books, or in conversation. 

These are in general very indistinctly described, and 
confusedly enumerated. 

We hear persons speaking of " Syllogistic Reasoning," 
and such as is not " Syllogistic ;" — of " Categorical, or 
Hypothetical Arguments," — or "Demonstrative, and Pro- 
bable, [or Moral] Pteasoning ;" of " Direct and Indirect 
Arguments ;"— of " A priori Arguments," " Arguments from 
Testimony," — from " Analogy," — from " Example" — by 
" Parity-of-Ileasoning," &e., without any distinct account 
being given of these and other modes of procedure. 

In reality, to enumerate thus confusedly the several kinds 
of Argument, is to commit the fault formerly noticed in 
reference to " cross-divisions;" there being, in this instance, 
no less than four different divisions ; which ought not to 
be blended together. 

First. The division of Arguments into irregular and 
syllogistic, and of Syllogisms again, into Categorical and 
Hypothetical, &c, is a division, strictly speaking, not 
of Arguments themselves, but of the forms of stating an 
argument. Por it is manifest (as above explained) that 
one individual argument may be stated in a Hypothetical 
or in a Categorical form, and in the first Figure, or in 
the second, <fcc. 

Secondly. The division of Arguments into probable and 
demonstrative is evidently according to the subject-matter: 
and is strictly, not a division of Arguments, considered as 
arguments, but rather, of the Propositions they consist of, 
in respect of the '•matter" of those propositions. 

§ 4. Thirdly. Arguments arc divided into "direct" and 
u indirect f according as your object is to establish either 
the truth of the Conclusion, or the falsity [the " Contra- 
dictory"] of one of the premises. For when we arrive by 
sound reasoning, at a false Conclusion, it is plain that one 
at least of the Premises must be false. 

In short, every valid argument may be stated in the 
form of a Conditional Proposition; "If the Premises are 
true, the Conclusion is true;" then, supposing you admit 
the Premises to be true, you must admit the truth of the 



Lesson xvii.] two classes of arguments. 137 

Conclusion; (which corresponds to a Constructive Condi- 
tional-syllogism;) and hence also, supposing you find the 
Conclusion false, you must admit that the Premises, or 
one of them, cannot but be false ; since if they were both 
true, the Conclusion would be true : and this corresponds 
to a Destructive Conditional-syllogism. 

Now the above is evidently a Division, not strictly 
speaking, of Arguments, but of the purposes for which any 
Argument may be designed : namely, either to prove its 
Conclusion, or to disprove one its Premises. 

For the same individual Argument may answer both 
purposes in different persons. For instance, "Whatever is 
maintained by the Stoics (or by such and such a philoso- 
pher, sect, party, &c.) must be admitted; that pain is no 
evil (or such and such a doctrine, whatever it may be, 
in each instance) is so maintained: therefore this must 
be admitted :" now a zealous partizan would be so fully 
convinced of the Premises that he will assent to the Con- 
clusion : others may be so revolted by the Conclusion, 
that they will thereupon reject the Major-premise. 

The Argument therefore will, to the one, be "direct," 
and to the other "indirect." 

§ 5. Fourthly. When we speak of arguing from a Cause 
to an Effect, or of arguing from Testimony to the truth 
of what is attested, or again, from a Icnoicn case to an 
unknown similar case, etc., these kinds of arguments are 
distinguished from each other "according to the relation 
existing between the Premises and the Conclusion, in respect 
of the subject-matter of each." 

This then, and this alone, is properly a division of 
Arguments,' as such. 

When we say, for instance, that in arguing from the 
"fall of rain" to the consequent "wetness of the roads," the 
i Premise is a Cause, and the Conclusion drawn, an Effect, 
it is evident we are not speaking of the more syllogistic 
connexion of the Premise and Conclusion ; (which, as was 
formerly explained, is always the same ;) nor again are we 
speaking of the subject-matter of those Propositions (as in 
the second Head) considered, — each by itself — merely as 
Propositions, independently of the Argument, for "Cause," 
and "Effect" are "relative words: and the Premise is called 



138 DIFFERENT KINDS OF ARGUMENTS. [Part V. 

a Cause q/that Effect which is inferred in the Conclusion. 
So that it is the relation, in respect of matter, of the 
Premise to the Conclusion, that we are speaking of. 

And so also in respect of Arguments from Testimony, 
and the other kinds that have been alluded to. 

§ 6. Arguments, then, may be divided, first, into two 
classes : First, such as might have been used to account 
for the Conclusion, supposing it had been already granted; 
and secondly, those which could not. Or, in other words, 
first, Arguments from Cause to Effect ; and, secondly, all 
other kinds. 

For instance, if I infer from a "fall of rain" that "the 
roads must be wet/' I am using an Argument of the "former 
Class [an "A-priori- Argument"]; since if it were known, 
and remarked by any one, that the roads are wet, I should 
account for that fact by informing him that it had rained. 

Or again, if a person were known to have committed a 
murder, and it were inquired how he came to perpetrate 
such a crime, then, any one would be said to account for it, 
[to show why he did it,*] by saying that he was a man of 
ferocious and revengeful character; or that he was known 
to bear malice against the deceased ; or to have an interest 
in his death, fcc. And these very circumstances might 
have been used (supposing the charge not proved) as an 
argument to cast suspicion on him. 

On the other hand, if his guilt were inferred from the 
testimony of some witnesses, or again, from his clothes 
having been bloody, or from his having about him some 
property of the deceased, these would be arguments of 
the other class, since they are such as could not have been 
employed to account for the fact, supposing it established. 

§ 7. The Arguments of this latter class may be subdi- 
vided into two kinds : which may be called Arguments 
from "Sign," and arguments from "Example" [or, "In- 
stance;"] each of which may also be further subdivided. 

i. As far as any circumstance is what may be called a 
"Condition" — more or less necessary — to the existence of 
a certain effect, phenomenon, event, result, law, &c. — in 



* It is to be observed, that the word "why" has three different senses: vi 
from what caus$ '< by what proofs ? for what purpose ? 



Lesson xvii.J arguments from sign. 139 

other words, as far as it is a "Condition" of the truth of 
some assertion or supposition, — so far it (the "condition") 
may be inferred [or "concluded"] from the truth of that as- 
sertion or supposition, — from the existence of that effect, &c. 

If it be a "Condition" absolutely essential to something 
which we know or assume to be true, it may of course be 
inferred with complete certainty ; and the nearer we ap- 
proach to this case, the stronger will be the probability. 

Thus, in the instance just above, when a man is sus- 
pected of a murder, from being found near the spot, his 
clothes bloody, and property of the deceased about him ; 
the perpetration of the murder by him is just so far proba- 
ble, as it is presumed to be a Condition of the existence of 
the "Signs;" i. e. so far as it is presumed that otherwise his 
clothes would not have been stained, &e. [or that they would 
not have been stained unless he had committed the deed.] 

So also the wetness of the roads is a " Sign" that rain 
has fallen, just so far as we suppose that otherwise the 
roads would not have been wet ; in short, that the fall of 
rain was a condition of that wetness. 

To this head we may refer all mathematical reasonings. 
Every property, for instance, of a triangle may be regard- 
ed as a "condition" of the supposition that a "Triangle" 
is what is defined. A figure would not be a Triangle, 
unless its angles were equal to right angles, &c. 

It is to be observed that although in many Arguments 
from "Sign" — as when we infer wetness of the roads from 
a fall of rain — we infer a Cause from an Effect, this is 
not inasmuch as [or "so far forth as"] it is a Cause, but 
inasmuch as it is a Condition. For we should no less 
infer from finding a certain spot wet, that it had been left 
uncovered ; though the mere absence of covering could not 
be properly called a Cause of its wetness. 

And in a like manner, a man's having been alive on a 
certain day, might be inferred as a necessary "Condition" 
(though certainly not a " Cause") of his dying the next day. 

§ 8. "Testimony''' is one kind of "Sign." For it evidently 
has weight just so far as we suppose the truth of what is 
attested to be a necessary "Condition" of the testimony; 
that is, just so far as we suppose that the testimony would 
not have been given, unless the thing attested had been true. 



140 DIFFERENT KINDS OF ARGUMENTS. [Part V. 

The different degrees of weight due to different Testi- 
monies must of course depend on a great variety of circum- 
stances; of which we must, on each occasion, judge in great 
measure from the particulars of the case then before as. 

There are two remarks, however, on this point which are 
needful to be kept in mind : first, we should remember the 
difference between Testimony to "matters-of;/ac£" and to 
"matters-of-opmiVm." When the question is about a fact, 
we look, merely or chiefly, to the honesty of the witness, 
and to his means of obtaining information; when the 
question relates to doctrine [or opinion] of any kind, his 
ability to judge must equally be taken into account. 

By a "matter [or " question"] of fact," is commonly un- 
derstood something which might, conceivably, be submitted 
to the senses; and about which it is supposed there could 
be no disagreement between persons who should be pre- 
sent, and to whose senses it should be submitted. 

By a "matter of opinion" again, is meant anything where- 
on an exercise oi judgment would be called for on the part 
of persons having the same objects presented to their senses; 
and who might conceivably disagree in their judgment. 

Suppose, for instance, a man is accused of a murder; 
whether he did or did not strike the blow, or fire the shot, &c. 
would be a "question oi fact" whether he did so wilfully 
and maliciously [which is necessary to constitute an act, 
murder\ would be a question of ["judgment," or] ojnnion. 

And observe, that the distinction does not at all turn on 
the greater or less degree of certainty attainable in the two 
cases respectively. For instance, whether "King Richard 
the Third, did, or did not put to death his nephews in the 
Tower, (which is a "question of fact") is very doubtful, 
and a matter of dispute among Historians : but what sort 
of an act it was, if he did commit it, is a " matte r-of-opin- 
ion," but one on which no one would be likely to doubt. 

§ 9. In most cases this distinction is very obvious; but 
it sometimes happens that a person is supposed, — and 
supposes himself — to be attesting a fact; when in truth 
he is giving an ojnnion; that is, either stating the infer- 
ence he draws from the fact he has witnessed; or again, 
professing to attest a fact which he has not really wit- 
nessed, but which he concludes to have taken place, from 
something he did witness. 



Lesson xvii.] matter-of-opxnion. 141 

An instance of the former kind is, when some one who 
is in attendance on a sick person bears witness that the 
patient was benefited, or was disordered, by taking such 
and such a medicine. He was an eyewitness perhaps, of 
the medicine's being swallowed, and of the subsequent 
change, for the better or for the worse ; but that the medi- 
cine caused that change (though he may be very right in 
believing that it did) is evidently his judgment. 

As an instance of the other kind, a man, suppose, will 
attest that he saw such a one killed; though perhaps he 
did not see him dead ; but saw him receive a wound 
which he judged (perhaps very rightly) could not fail to 
occasion speedy death. 

For it is to be remembered that there may be, and 
often are " questions-of opinion " relative to facts; i. e., we 
judge from such and such circumstances, that so and so is, 
or is not, likely to occur ; or to exist. It is a fact, that 
there is, or that there is not, a great lake in the interior 
of New Holland ; but till that interior shall have been 
explored, everyone is left to form his opinion, and to 
judge according to probabilities. 

And hence, it should also be remembered, that men 
are apt to reason unconsciously ; and thus to suppose 
themselves bearing testimony (as has been said) to some- 
thing their senses have witnessed, when in truth they are 
stating their own inferences therefrom. 

The process which usually takes place is this: their 
senses furnish them with one Premise, (the Minor,) 
the other is supplied by their own mind; and the Con- 
clusion drawn from these two (as you may see in the 
above examples) is what they describe themselves as 
having vjitnessed. 

§ 10. ii. The other remark to be borne in mind, is, 
that when several independent witnesses [witnesses be- 
tween whom there could have been no collusion J attest the 
same thing, the weight of their testimony depends on this 
agreement, and not on the weight of each considered sepa- 
rately, or on the mere addition of these together. 

Thus, if a stranger, or one on whose veracity I have no 
reliance, gives me intelligence of some remarkable trans- 
action, or state of things, which he professes to have wit- 



142 DIFFERENT KINDS OF ARGUMENTS. [Part V. 

nessed, describing fully all the details, I may perhaps 
think it more likely than not that the whole story and 
all the particulars are a fabrication. But if I receive 
the same account from another, and again from another 
person, (equally undeserving of credit,) who could not 
have had any communication with the first, nor could 
have had access to any source of false information com- 
mon to them all, I should at once believe them; because 
the chances would be immeasurably great against several 
persons, (however likely, each, to invent a story) having 
independently, invented the same story. 

And the force of evidence in such an argument depends 
mainly on the number and minuteness of the particulars 
in the thing attested; because the chances are thus in- 
creased against an accidental coincidence. 

The same rule applies not only to "Testimony" but to 
other "Signs" also. As when, (to refer to an example in 
the preceding Lesson,) a person after swallowing a cer- 
tain drug is attacked with such and such symptoms; 
which may have been accidental; if the same symptoms 
follow in another case, and another, &c, we are convinced 
at length that these cannot have been accidental coinci- 
dences, but that the drug caused the symptoms. 

§11. When we reason from a known case to another, 
or others, less known, under the same Class, this is called 
arguing from "Example" — by "Induction" — from "Expe- 
rience" — by "Analogy" — by "Parity -of-reasoning," &c.,all 
of which expressions, though not exactly synonymous, 
denote a process substantially the same. And the two 
cases, — the known and the unknown, — are said to be 
"analogous" or "parallel cases;" the common Class which 
they both fall under being the point of Resemblance or 
Analogy between the two. 

Thus, we show from the example of the French Revo- 
lution, and that of England in the time of Charles the 
Eirst, that the extreme of Democracy is likely to lead to 
a military Monarchy. 

It is in this sense that we speak of "making an Ex- 
ample" of one who is punished for any faults; so as to 
deter others by the expectation that a like fault in them 
will lead to their punishment. 



Lesson xvii.] argument by induction. 143 

And it is thus that we learn to anticipate such and 
such weather, in certain situations, at certain seasons ; 
and in short, become acquainted with the general Laws 
of Nature. 

In all these cases, we proceed, strictly speaking, by- Ana- 
logy. But this word is most usually employed in those 
arguments where the correspondence between the two cases 
is not so complete as to warrant a certainty in our conclu- 
sions. When the two cases do correspond completely, or 
nearly so, wo usually employ the word Experience. 

Thus a man would be said to be convinced from " Expe- 
rience" that such and such a kind of diet, or of medicine, 
or of weather, is wholesome or unwholesome to himself; 
if he had invariably observed like effects on a number 
of men, he might perhaps speak of experience as having 
convinced him that this diet, &c, was wholesome or un- 
wholesome for the whole human Species \ though in this, 
he would be liable to mistake ; but if he conjectured the 
same with respect to some other Species of animal, every 
one would say he was reasoning by "Analogy." 

§ 12. And here observe, that it is not strictly correct to 
speak of " Knowing by Experience" such and such a general 
-truth; or that so and so will take place under such and such 
circumstances. ISTot but that we may often have the most 
complete and rational assurance of general truths, or future 
events; but, properly speaking, what we knoiv by " expe- 
rience," is the past only ; and those individual events 
which we have actually experienced: and any conviction 
concerning a general rule and concerning future occur- 
rences, is what we judge from Experience.* 

And this distinction is important to be remembered, 
because, although (as we have said) there are numberless 
cases in which the conclusion thus drawn is not liable to 
mistake, many persons are apt — as was above remarked — 
to make mistakes as to what it is that they themselves, — 
or that others, — are, on each occasion, bearing witness to. 

A mere fact, or a number of individual facts, however 
strange they may seem to us, — that are attested by a per- 
son whose veracity we can fully rely on, we are justified 



* Seethe instance formerly cited from Hume, of the argument that " miracles 
are contrary to experience," &c 



144 DIFFERED KINDS OF ARGUMENTS. [Part V. 

in believing, even though, he be a man of no superior 
judgment. But if he states some general fact [or "law"] 
as a thing experienced by him, we should remember that 
this is his inference, from his experience. It may be a 
very correct one: and it may be one in which no great 
ability is needed for forming a correct judgment; but still 
the case is one in which his ability, as well as veracity, is 
to be taken into account. 

For instance, a Farmer or a Gardener will tell you that 
he "knows by experience" that such and such a crop suc- 
ceeds best if sown in Autumn, and such a crop again, if 
sown in Spring. And in most instances they will be right: 
that is, their Experience will have led them to right con- 
clusions. But what they have actually known by experience, 
is, the success or the failure of certain individual crops. 

And it is remarkable, that for many Ages all Farmers 
and Gardeners without exception were no less firmly con- 
vinced — and convinced of their knowing it by experience 
— that the crops would never turn out good unless the 
seed were sown during the increase of the Moon; a belief 
which is now completely exploded, except in some remote 
and unenlightened districts. 

§ 13. In all cases, Arguments of the Class we are now 
speaking of, proceed on the supposition (which is the 
Major-premise) that "what takes place, — or has happened 
— or which we are sure would happen — in a certain case, 
must happen, or take place, in a certain other similar [or 
analogous] case; or in all such cases." 

The degrees of probability of this Major-premise will 
of course be infinitely various, according to the subject- 
matter. In the investigation of what are called "physical- 
laws," a single experiment, fairly and carefully made, is 
often allowed to be conclusive; because we can often ascer- 
tain all the circumstances connected with the experiment. 
Thus a Chemist, who should have ascertained by trial, 
that a specimen of Gold, or of some other metal before 
him, would combine with Mercury, would at once con- 
clude this to be a property of that metal universally. 

In human transactions, on the contrary, it would be 
thought very rash to draw a conclusion from a single oc- 
currence; or even from two or three. We make, in such 



Lesson xvii] invented example. 145 

cases, a wide "Induction" (as it is called) of a number of 
individual instances, [or " examples,"] before we venture 
to conclude universally, — or even as a general rule — what 
is likly to be, for instance, the result of such and such 
a form of Government, — of the existence of Slavery, — of 
the diffusion of Education, — of Manufactories, &c. 

§ 14. We have said that we sometimes argue not only 
from what has actually happened in certain cases, but also 
from what we feel certain would happen in such and such a 
supposed case. Of this description are instructive "Fables" 
[or "Parables," "Apologues," "Illustrations"] in which a 
general maxim [or "principle"] is inferred from a supposed 
case, analogous to that to which we mean to apply the maxim. 

Thus, the imprudence of a man who should hastily 
join the desciples of Jesus, without having calculated the 
sacrifices required, and the fortitude expected of him, is 
illustrated by the supposed case of a man's beginning to 
build a house without computing the cost. 

So also Socrates argued against the practice of some of 
the Greek republics, who chose their magistrates by lot f 
from the supposed case of mariners casting lots ivho 
should have the management of the vessel, instead of 
choosing the best Seaman. 

And Nathan's parable brought home to David a sense 
of the enormity of his own crime. Indeed, the " golden 
rule" of supposing yourself to change places with your 
neighbour, and reflecting what you would then think it 
right for him to do towards you, is merely an admoni- 
tion to employ in one (very numerous) class of cases, 
*uch a mode of reasoning. 

In every employment of what may be called ["fictitious," 
or] "invented example" [reasoning from a supposed case], 
the argument will manifestly have no weight, unless the 
result that is supposed in the imaginary case, be such as 
one would fully anticipate. 

On the other hand, real instances have weight, even 
though they be such as one would not have expected. For 
instance, that all animab with horna on the head should 
chew the cud, and should be destitute of upper cutting- 
teeth, is what no one would have originally conjectured; 
but extensive observation has so fully established this as a 
G 



146 DIFFERENT KINDS OF ARGUMENTS. [Part V. 

universal rule, that a naturalist, on finding the skeleton 
of some unknown animal with horns on the skull, would 
at once pronounce it a ruminant, and would be certain 
of the absence of upper incisors. 

§ 15. "When an Argument of the Class now before us, 
[from Example, Analogy, &c.] is opposed; by denial of one 
of the Premises, it is usual, in ordinary discourse, so say, 
either, "the statement is not correct" which is denying 
the -3/mor-premise, — or "this case does not apply" [or is 
"not hi 2>oint"~\ — or "does not hold good in reference to 
the one before us;" or "the cases are not parallel:" which 
amounts (as you will see on examination) to denying the 
Mcyor-preimse. 

Thus, if any one recommends to his patient a certain 
medicine, as having been found serviceable in cases of 
Typhus, it might be either denied that it did prove ser- 
viceable in those cases (which would be a denial of the 
Minor,) or again it might be denied that this patient's 
disorder is the same as those; which would be a denial 
of the ifo/or-premise. 

And here observe, that two things may be very unlike 
in most respects, and yet quite alike — i.e., the Analogy 
may hold good — in the one point that is essential to the 
argument : or, again, they may disagree in that one, 
though they are analogous in many other points. 

And it is from inattention to this distinction, that just 
arguments from Analogy are often rejected, and falla- 
cious ones admitted. 

§ 16. For instance, in the Parables alluded to above, 
if a man should object that "a lamb is a very different 
thing from a wife," and "a ship, from a Republic," the 
differences, every one would see, do not affect the 
Analogy in question. 

On the other hand, there is an Analogy in many re- 
spects between all " valuable Articles" that man uses ; as 
corn and iron or lead, and again (what are called the 
precious metals) gold and silver. And as an increased 
supply of most of these articles, while it lowered their 
price, would not diminish their usefulness, and would thus 
prove a general benefit, some might infer that this would 
hold good in respect of gold and silver. 



Lesson xvii.] conclusion. 147 

If the earth should yield two bushels of corn, or two 
tons of iron or lead, for one that it now yields, these 
articles would be much cheaper ; while a bushel of corn 
would be as useful in feeding us, as now; and so with 
most other articles. 

But if the supply of gold or silver were thus doubled, 
the chief use of these being for coin, and the utility of coin 
depending on its value, the only important change would 
be that a sovereign or a shilling would be twice as large 
as now^ and therefore twice as cumbrous. So that no 
advantage would result. 

It is manifest that in a train of Reasoning, it will often 
happen that several of the different kinds of argument 
we have spoken of will be combined. Thus we may per- 
haps have to prove by several Examples, the existence of 
a certain " Cause ;" and from tha,t cause to infer a certain 
" Effect;" and that effect again may be employed as a 
"Sign" to infer a certain "Condition," &c. 



In this, and the preceding Lessons, several interesting 
subjects have been very slightly touched on, which may 
be found more fully treated of, and the views now taken 
more developed, in treatises on those several subjects.* 

If you proceed, in following up this course of study, to 
peruse such treatises, you will have been prepared, it is 
hoped, to find that perusal the easier and the more inter- 
esting, from what has been explained in these Lessons : 
and you will be the better able to understand what is 
valuable, in other works on such subjects, and to detect 
anything that may be erroneous. 

* In the Elements of Rhetoric, Part L, the subjects of this last Lesson a»c 
more fully treated of. 



149 

INDEX. 

[To be made by the Student | 



Lesson. § Page. 



150 INDEX. 

Lesson. § Page. 



INDEX, 151 

Lesson. § Page. 



152 INDEX. 

Lesson. § Page. 



INDEX, 153 

Lesson, § Page, 



154 INDEX. 

Lesson. § Page. 



INDEX. 155 

Lesson. § Page. 



156 INDEX. 

Lesson. § Page. 



-. 



INDEX. 157 

Lesson. § Page. 



153 IHDEX. 

Lesson. § Page. 






INDEX. 150 

Lesson. § Page. 



160 INDEX* 



Lesson. § Page. 









" ; - 









v 

- 



<\ 



^ 







V * 












Deacidified using the Bookkeeper procesir 
Neutralizing agent: Magnesium Oxide 
Treatment Date: Sept. 2004 

PreservationTechnologies 



















V 5 *%> 



ff ! "A * 






% 



/ ^ 








> 












^f^^J^t^f^rJf^ 



111 



lit win timmuum 




Hi 



■ 



